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ISSN 1729-5254

 

For Issues (1-6), please contact the editor at: info[AT]ejtp.com.

 

Volume 2, Issue 7 (August 2005)

 

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Number 

Articles Title

Abstract

1

Application of Coadjoint Orbits in the Thermodynamics of Non-Compact Manifolds.

 

V. V. Mikheyev; I. V. Shirokov

 

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Method of the solution of the main problem of homogeneous spaces thermodynamics for non-compact spaces in the case of non-compact Lie groups is presented in the article. The method is based on the method of coadjoint orbits. The formula that allows efficiently evaluate heat kernel on non-compact spaces is obtained. The method is illustrated by non-trivial example.

2

The Boundary Conditions Geometry in Lattice-Ising Model

 

You-gang Feng

 

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We found that the differential topology of the lattice-system Ising model determines whether there can be the continuous phase transition, The geometric topology of the space the lattice-system is embedded in determines whether the system can become ordered. If the system becomes ordered it may not admit the continuous phase transition. The spin-projection orientations are strongly influenced by the geometric topology of the space the lattice system is embedded in.

3

Simulation of Ginger EPR Spectra Obtained by X-Irradiation: Quantum Approach

 

S. Laachir; M. Moussetad; R. Adhiri; A. Fahli; M. Aboulfatah; M. Mikou

 

 

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The ginger sample has been exposed to X-rays at cumulative doses. The foodstuffs irradiation is used in particular to improve their hygienic qualities and increase their shelf lives. This process has been approved by various international organizations: FAO -- AIEA -- WHO. In the present work, we propose to reproduce by simulation, based on a quantum approach, of the ESR (Electron Spin Resonance) spectra. The semi-classical approach is valid for a simple system, but not for a complex system such as an atom with hyperfine structure. In this case a quantum approach, based on spin Hamiltonian, is essential to interpret the ESR spectra. The main result is that the simulated spectra are in good agreement with the experimental ones obtained before and after irradiation.

4

 Quantum AdS1+3 Black Holes with Effective Cosmological Constant

 

 

El-Nabulsi Ahmad Rami

 

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A quantum AdS1+3 massive and massless black holes with effective cosmological constant induced from non-minimal coupling and supergravities arguments are constructed and discussed in details.

 

 Volume 2, Issue 8 (December 2005)

 

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Number 

Articles Title

Abstract

1

Fractional Unstable Euclidean Universe.

 

 El-Nabulsi Ahmad Rami

 

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Despite common acceptance of Big Bang hypothesis among most cosmologists, nonetheless there are criticisms from a small number of theorists partly supported by astronomy observation suggesting that redshift data could not always be attributed to cosmological expansion. In this paper, a new approach to cosmology fractional calculus has been developed that we hope will attract attention from astrophysicists and cosmologists because of the way it challenges the conventional big bang framework.

2

Parametric Relationships Among Some Phenomenological Non-Relativistic Hadronic Potentials

 

 

 

Teik-Cheng Lim

 

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In recent years, parametric relationships between interatomic potential energy functions have been developed in the realm of molecular chemistry and condensed matter physics. However, no parametric relationships have been developed so far among intra-atomic potentials. As an extension of previous works into the realm of intra-atomic potentials, we herein consider the possibility that hadronic potentials can be interrelated via their parameters. Hadronic potentials give quantitative description of interquark energy in terms of interquark distance, hence understanding how each potential function influences the theoretical modeling can be sought via knowledge of interrelationship amongst the potentials parameters. Phenomenological non-relativistic hadronic potentials are related amongst the mixed-powerlaw potential themselves, and with the Logarithmic potentials using calculus. Exact nonlinear relationships were obtained between the parameters whereby the interquark distance is included as one of the variables. It is also demonstrated that, when the interquark distance in the parametric relationships is assigned a fixed value of unity, the parametric relationships remain valid from the plotted potential energy curves..

3

Non Linear Assessment of Musical Consonance

 

SLluis Lligo˜na Trulla, Alessandro Giuliani, Giovanna Zimatore, Alfredo Colosimo and Joseph P. Zbilut

 

 

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The position of intervals and the degree of musical consonance can be objectively explained by temporal series formed by mixing two pure sounds covering an octave. This result is achieved by means of Recurrence Quantification Analysis (RQA) without considering neither overtones nor physiological hypotheses. The obtained prediction of a consonance can be considered a novel solution to Galileo's conjecture on the nature of consonance. It constitutes an objective link between musical performance and listeners hearing activity..

4

 Conditions for the Generation of Causal Paradoxes from Superluminal Signals

 

 

Giuseppe Russo

 

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We introduce a simple method to illustrate how the Lorentz transformation lead to causal loop paradoxes when they are applied to superluminal velocities.

 

Volume 3, Issue 9 (February 2006)

 

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Number 

Articles Title

Abstract

1

Spinning of Particles in Schwarzschild-de-Sitter and Schwarzschild-Anti-de-Sitter Space-Times with `Effective Cosmological Constant'.

 

 El-Nabulsi Ahmad Rami

 

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Spinning of particles in SdS and SAdS space-times with effective cosmological constant is discussed in details. It is shown that the equilibrium conditions are independent of the spin of the test particles and are satisfied only for particular conditions relating the Einstein's cosmological constant with the ultra-light masses implemented in the theory from supergravities arguments and non-minimal coupling.

2

How S-S' di Quark Pairs Signify an Einstein Constant Dominated Cosmology, and Lead to New Inflationary Cosmology Physics

 

 

A. W. Beckwith

 

 

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We review the results of a model of how nucleation of a new universe occurs, assuming a di quark identification for soliton-anti soliton constituent parts of a scalar field. Initially, we employ a false vacuum potential system; however, when cosmological expansion is dominated by the Einstein cosmological constant at the end of chaotic inflation, the initial di quark scalar field is not consistent w.r.t a semi classical consistency condition we analyze as the potential changes to the chaotic inflationary potential utilized by Guth. We use Scherrer's derivation of a sound speed being zero during initial inflationary cosmology, and obtain a sound speed approaching unity ~as the slope of the scalar field moves away from a thin wall approximation. All this is to aid in a data reconstruction problem of how to account for the initial origins of CMB due to dark matter since effective field theories as presently constructed require a cut off value for applicability of their potential structure. This is often at the cost of, especially in early universe theoretical models, of clearly defined baryogenesis, and of a well defined mechanism of phase transitions.

3

Vectorial Lorentz Transformations

 

 

 

 

Jorge A. Franco R.

 

 

 

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We have noticed in relativistic literature that the derivation of Lorentz Transformations (LT) usually is presented by confining the moving system O' to move along the X-axis, namely, as a particular case of a more general movement. When this movement is generalized different transformations are obtained (which is a contradiction by itself) and a hidden vectorial characteristic of time is revealed. LT have been generalized in order to solve some physical and mathematical inconsistencies, such as the dissimilar manners (transversal, longitudinal) the particle's shape is influenced by its velocity and LT's inconsistency with Maxwell equations when in its derivation the pulse of light is sent perpendicular to the displacement of the moving system O'. Unlike the canonical derivation of LT, in the undertaken development of the generalized LT, assumptions were not used. Practical applications of generalized Vectorial Lorentz Transformations (VLT) were undertaken and as outcome a new definition of Local Lorentz Transformations (LLT) of magnitudes appeared. As another consequence, a characteristic and unique scaling Lorentz factor was obtained for each magnitude Given this, a dimensional analysis based upon these Lorentz factors came up. In addition, dynamical transformations were obtained and a new definition of mass was found.

4

Lattice Dynamics of Hydrogen Interstice Co_{0.92}Fe_{0.08}

 

 

C. Kalai Arasi, R. John Bosco Balaguru, S. Alfred Cecil Raj, and N. Lawrence

 

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Lattice dynamics of hydrogen interstice in the binary alloy Co_{0.92} Fe _{0.08} has been carried out to calculate the phonon dispersions along the [100], [110], [111] directions. The phonon density of states, variation of specific heat capacity and Debye's temperature with temperature are also calculated. A reasonably good agreement is found between the calculated and other theoretical and experimental results. The mean square displacement (MSD) of atoms surrounding the interstitial hydrogen atom is reported along with the defect modes.

5

Petrov classification of the conformal tensor

 

M. A. Acevedo M., M. Enciso-Aguilar, and J. Lopez-Bonilla

 

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We exhibit a flux diagram in its tensorial and Newman-Penrose representations for the Petrov classification.

6

On Inflation Potentials in Randall-Sundrum Braneworld Model

 

M.Bennai, H.Chakir, and Z.Sakhi

 

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We study the inflationary dynamics of the universe in the Randall-Sandrum typeII Braneworld model. We consider both an inverse-power law and exponential potentials and apply the Slow-Roll approximation in high energy limit to derive analytical expression of relevant inflationary quantities. An upper bound for the coupling constant was also obtained and a numerical value of perturbation spectrum is calculated in good agreement with observation.

7

Considerations About The Anomalous Efficiency Of Particular Thermodynamic Cycles

 

 

 

Leonardo Chiatti

 

 

 

 

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Some years ago Vignati (refs. 1, 2, 3) showed that, under some particular circumstances (inter alia isobaric processes connected through internal heat exchangers), the efficiency of an Ericsson cycle involving a real gas can exceed the Carnot limit \eta_{C} , in contradiction with the second principle of thermodynamics. However, the convergence of Vignati's algorithm, giving the temperature difference between the intermediate heat exchangers, has not yet been proved. In particular, it isn't clear, if the number of intermediate heat exchangers infinitely increases, the condition of a total (perfect) heat recovery may be asymptotically approximated. This remark is relevant because the claimed anomalous efficiencies appear only in the limit of a perfect heat recovery. Considering a suitable counterexample, we prove that, in general, the residual heat discharged on the external sources does not vanish in that limit, even when the isobars exchange the same amount of heat. Therefore the violation of the second law inferred from Vignati's calculation is merely apparent, being referred to a situation which is not (in principle) physically realisable. The essentials of the Vignati's argument are then applied to an Ericsson cycle involving an ideal gas undergoing chemical reactions. Again, no contradiction arises with the second principle.

 

Volume 3, Issue 10 (April 2006), Majorana Issue (Editor: Ignazio Licata)

 

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Number 

Articles Title

Abstract

 

Majorana Imoact on Contemporary Physics

 

Ignazio Licata

 

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Editorial Note

1

The Scientific Work Of Ettore Majorana: An Introduction

 

Erasmo Recami

 

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A Brief bibliography of the scientific work of Ettore Majorana has been discussed.

2

On the Hamiltonian Form of Generalized Dirac Equation for Fermions with Two Mass States

 

Sergey. I. Kruglov

 

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Dynamical and non-dynamical components of the 20-component wave function are separated in the generalized Dirac equation of the first order, describing fermions with spin 1/2 and two mass states. After the exclusion of the non-dynamical components, we obtain the Hamiltonian Form of equations. Minimal and non-minimal electromagnetic interactions of particles are considered here.

 

3

Majorana Equation and exotics: Higher Derivative Models, Anyons and Noncommutative Geometry

 

Mikhail S. Plyushchay

 

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In 1932 Ettore Majorana proposed an infinite-component relativistic wave equation for particles of arbitrary integer and half-integer spin. In the late 80s and early 90s it was found that the higher-derivative geometric particle models underlie the Majorana equation, and that its (2+1)-dimensional analogue provides with a natural basis for the description of relativistic anyons. We review these aspects and discuss the relationship of the equation to the exotic planar Galilei symmetry and noncommutative geometry. We also point out the relation of some Abelian gauge field theories with Chern-Simons terms to the Landau problem in the noncommutative plane from the perspective of the Majorana equation.

 

 

4

Wave Equations, Renormalization and Meaning of the Planck's Mass: Some Qualitative Considerations

 

 

Leonardo Chiatti

 

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The five-dimensional version of the quantum relativistic Klein-Gordon wave equation is assumed to be a more fundamental description for the dynamics of the single particle without spin. The meaning of the renormalization procedure in QFT and the Planck's mass one are briefly discussed from this point of view.

 

5

Nonlinear Field Equations and Solitons as Particles

 

Attilio Maccari

 

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Profound advances have recently interested nonlinear field theories and their exact or approximate solutions. We review the last results and point out some important unresolved questions. It is well known that quantum field theories are based upon Fourier series and the identification of plane waves with free particles. On the contrary, nonlinear field theories admit the existence of coherent solutions (dromions, solitons and so on). Moreover, one can construct lower dimensional chaotic patterns, periodic-chaotic patterns, chaotic soliton and dromion patterns. In a similar way, fractal dromion and lump patterns as well as stochastic fractal excitations can appear in the solution. We discuss in some detail a nonlinear Dirac field and a spontaneous symmetry breaking model that are reduced by means of the asymptotic perturbation method to a system of nonlinear evolution equations integrable via an appropriate change of variables. Their coherent, chaotic and fractal solutions are examined in some detail. Finally, we consider the possible identification of some types of coherent solutions with extended particles along the de Broglie-Bohm theory. However, the last findings suggest an inadequacy of the particle concept that appears only as a particular case of nonlinear field theories excitations.

 

6

The Quantum Character of Physical Fields.

Foundations of Field Theories

 

Ludmila. I. Petrova

 

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The existing field theories are based on the properties of closed exterior forms, which are invariant ones and correspond to conservation laws for physical fields. Hence, to understand the foundations of field theories and their unity, one has to know how such closed exterior forms are obtained. In the present paper it is shown that closed exterior forms corresponding to field theories are obtained from the equations modeling conservation (balance) laws for material media. It has been developed the evolutionary method that enables one to describe the process of obtaining closed exterior forms. The process of obtaining closed exterior forms discloses the mechanism of evolutionary processes in material media and shows that material media generate, discretely, the physical structures, from which the physical fields are formed. This justifies the quantum character of field theories. On the other hand, this process demonstrates the connection between field theories and the equations for material media and points to the fact that the foundations of field theories must be conditioned by the properties of material media. It is shown that the external and internal symmetries of field theories are conditioned by the degrees of freedom of material media. The classification parameter of physical fields and interactions, that is, the parameter of the unified field theory, is connected with the number of noncommutative balance conservation laws for material media.

 

7

Relativistic Causality and

Quasi -Orthomodular Algebras

 

 

Renato.Nobili

 

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The concept of fractionability or decomposability in parts of a physical system has its mathematical counterpart in the lattice--theoretic concept of orthomodularity. Systems with a finite number of degrees of freedom can be decomposed in different ways, corresponding to different groupings of the degrees of freedom. The orthomodular structure of these simple systems is trivially manifest. The problem then arises as to whether the same property is shared by physical systems with an infinite number of degrees of freedom, in particular by the quantum relativistic ones. The latter case was approached several years ago by Haag and Schroer (1962; Haag, 1992) who started from noting that the causally complete sets of Minkowski spacetime form an orthomodular lattice and posed the question of whether the subalgebras of local observables, with topological supports on such subsets, form themselves a corresponding orthomodular lattice. Were it so, the way would be paved to interpreting spacetime as an intrinsic property of a local quantum field algebra. Surprisingly enough, however, the hoped property does not hold for local algebras of free fields with superselection rules. The possibility seems to be instead open if the local currents that govern the superselection rules are driven by gauge fields. Thus, in the framework of local quantum physics, the request for algebraic orthomodularity seems to imply physical interactions! Despite its charm, however, such a request appears plagued by ambiguities and criticities that make of it an ill--posed problem. The proposers themselves, indeed, concluded that the orthomodular correspondence hypothesis is too strong for having a chance of being practicable. Thus, neither the idea was taken seriously by the proposers nor further investigated by others up to a reasonable degree of clarification. This paper is an attempt to re--formulate and well--pose the problem. It will be shown that the idea is viable provided that the algebra of local observables: (1) is considered all over the whole range of its irreducible representations; (2) is widened with the addition of the elements of a suitable intertwining group of automorphisms; (3) the orthomodular correspondence requirement is modified to an extent sufficient to impart a natural topological structure to the intertwined algebra of observables so obtained. A novel scenario then emerges in which local quantum physics appears to provide a general framework for non--perturbative quantum field dynamics.

 

8

Lorentz Invariant Majorana Formulation of Electrodynamics in the Clifford Algebra Formalism

 

 

Tomislav Ivezic

 

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In this paper we present a new geometric formulation (Clifford algebra formalism) of the field equations, which is independent of the reference frame and of the chosen system of coordinates in it. This formulation deals with the complex 1-vector \Psi =E-icB (i is the unit imaginary), which is four-dimensional (4D) geometric generalization of Majorana's complex 3D quantity \Psi }=E-icB. When the sources are absent the field equations with the complex \Psi become Dirac-like relativistic wave equations for the free photon. In the frame of ``fiducial'' observers (the observers who measure fields are at rest) and in the standard basis the component form of the field equations with 4D \Psi reproduces the component form of Majorana-Maxwell equations with 3D field \Psi . The important differences between the approach with the 4D \Psi and that one with the 3D \Psi are discussed.

 

9

" Anticoherent " Spin States via the Majorana Representation

 

 

Jason Zimba

 

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In this article we define and exhibit '' anticoherent" spin states, which are in a sense '' the opposite" of the familiar coherent spin states. Since the familiar coherent states are as "classical" as spin states can be, the anticoherent states may turn out to be better candidates for applications involving non-classical behaviors such as quantum entanglement. Thanks to the Majorana representation of spinors as 2s-tuples of points on the Riemann sphere, classes of anticoherent states are easy to find; the development of such examples also leads us into some curious geometry involving the perfect solids.

 

10

Stretching the Electron as Far as it Will Go

 

 

G. W. Semenoff and P. Sodano

 

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Effects associated with the existence of isolated zero modes of Majorana fermions are discussed. It is argued that the quantization of this system necessarily contains highly extended quantum states and that populating and depopulating such states by interacting with the quantum system leads to long-ranged teleportation-like processes. Also leads to spontaneous violation of fermion parity symmetry. A quasi-realistic model consisting of a quantum wire embedded in a p-wave superconductor is discussed as an explicit example of a physical system with an isolated Majorana zero mode.

 

11

Why do Majorana Neutrinos Run Faster than Dirac Neutrinos?

 

 

Zhi-zhong Xing and He Zhang

 

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The \tau-lepton dominance in the one-loop renormalization-group equations (RGEs) of neutrinos sets a cute criterion to parametrize the 3x3 lepton flavor mixing matrix U: its elements U_{3i} (for i=1,2,3) should be as simple as possible. Such a novel parametrization is different from the ``standard" one used in the literature and can lead to greatly simplified RGEs for three mixing angles and the physical CP-violating phase(s), no matter whether neutrinos are Dirac or Majorana particles. We show that the RGEs of Dirac neutrinos are not identical with those of Majorana neutrinos even if two Majorana CP-violating phases vanish. As the latter can keep vanishing from the electroweak scale to the typical seesaw scale, it makes sense to explore the similarities and differences between the RGE running effects of Dirac and Majorana neutrinos. We conclude that Majorana neutrinos are in general expected to run faster (i.e., more significantly) than Dirac neutrinos.

 

12

Universe Without Singularities

A Group Approach to De Sitter Cosmology

 

Ignazio Licata

 

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In the last years the traditional scenario of ``Big Bang'' has been deeply modified by the study of the quantum features of the Universe evolution, proposing again the problem of using ``local'' physical laws on cosmic scale, with particular regard to the cosmological constant role. The ``group extention'' method shows that the De Sitter group univocally generalizes the Poincaré group, formally justifies the cosmological constant use and suggests a new interpretation for Hartle-Hawking boundary conditions in Quantum Cosmology.

 

13

Majorana and the Investigation of Infrared Spectra of Ammonia

 

Elisabetta. Di Grezia

 

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An account is given on the first studies on the physics of ammonia, focusing on the infrared spectra of that molecule. Relevant contributions from several authors, in the years until 1932, are pointed out, discussing also an unknown study by E.Majorana on this topic.

 

14

Exact Solution of Majorana Equation via Heaviside Operational Ansatz

 

 

Valentino A. Simpao

 

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In context of a transformation between Majorana and Dirac wavefunctions, it suffices to solve the related interactive Dirac problem and then apply the transformation of variables on the Dirac wavefunction in order to obtain the Majorana wavefunction of the given Majorana equation. Clearly, this connection between solutions continues to hold if the free Majorana and Dirac equations are each coupled to an external gauge field [e.g., Electromagnetism] via the minimum coupling prescription. Applying the formal solution scheme Heaviside Operational Ansatz[heretofore, HOA] put forward in [ EJTP 1 (2004), 10-16], provides an exact quadrature solution for the massive minimum-coupled Majorana equation in terms of the solution of the corresponding massive minimum-coupled Dirac equation.

 

15

A Logical Analysis of Majorana’s Papers on Theoretical Physics

 

 

A. Drago and S. Esposito

 

 

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We study two celebrated Majorana's papers through a method of investigation which relies upon the recently recognized distinction between classical logic and several kinds of non-classical logics, i.e. the failure of the double negation law. This law fails when a double negated sentence is not equivalent to the corresponding positive sentence, owing to the lack of scientific evidence of the latter one. All recognized double negated sentences inside the text of each paper are listed; the mere sequence of such sentences giving the logical thread of Majorana's arguing. This one is recognized to be of the Lagrangian kind, which mixes logical arguing and mathematical calculation; i.e. the author puts a fundamental problem which is solved by anticipating the mathematical hypothesis able to solve it, and then by drawing from this hypothesis the mathematical consequences in order to reach to desired result. Furthermore the rethoric of presentation used by Majorana results to be a juridical one, owing to his style of presenting the laws to which an ideal theoretical physicist has to conform his mind in order to solve the problem at issue.

 

16

Four Variations on Theoretical Physics by Ettore Majorana

 

 

Salvatore. Esposito

 

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An account is given of some topical unpublished work by Ettore Majorana, revealing his very deep intuitions and skillfulness in Theoretical Physics. The relevance of the quite unknown results obtained by him is pointed out as well.

 

17

The Majorana Oscillator

 

 

Eliano Pessa

 

 

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At present the expression ‘Majorana oscillator’ does not appear to be in use in theoretical physics. However, the author of this paper heard it in the Seventies, during private conversations with the late Prof. B.Touschek. This little contribution tries to explore the possible meanings of this expression and introduces a new field equation, generalizing the one already introduced by Majorana himself, which could describe a hypothetical ‘Majorana oscillator’.

 

18

Scattering of an \alpha Particle by a Radioactive Nucleus

 

Unpublished 1928

 

Ettore Majorana

 

 

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In the following we reproduce, translated into English, a section of Volumetto II, a notebook written by Majorana in 1928 when he was still a Physics student at the University of Rome (see S. Esposito, E. Majorana jr, A. van der Merwe and E. Recami (eds.) Ettore Majorana: Notes on Theoretical Physics, Kluwer, New York, 2003). This study was performed by the author when he was preparing his Thesis work on ``The Quantum Theory of Radioactive Nuclei'' (unpublished), whose supervisor was E. Fermi.

 

S. Esposito

 

19

Comments on a Paper by Majorana Concerning Elementary Particles

 

 

 

David. M. Fradkin

 

 

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An early paper (1932) by Majorana, that has received but scant attention, is reexamined in light of later developments. This pioneering paper constructs a relativistically invariant theory of arbitrary spin particles, develops and utilizes infinite dimensional representations of the homogeneous Lorentz group, and provides a mass spectrum for elementary particles. The relevance of Majorana’s approach and results to later and current research is explained.

 

Reprinted with permission from the AMERICAN JOURNAL OF PHYSICS, Volume 34, Issue 4, pp. 314-318. Copyright 1966, American Association of Physics Teachers

 

We reproduce here the historical D. M. Fradkin 1966 paper whose role among the physicists of high energy was decisive; since then espressions like "Majorana mass", "Majorana spinors" and "Majorana neutrino" have become usual. The paper is based upon the work Teoria di Particelle con Momento Intrinseco Arbitrario, translated by Italiam from Edoardo Amaldi.

 

Ignazio Licata

 

 

 

 

Volume 3, Issue 11 (June 2006)

 

Full text: Acrobat PDF (2,349 KB)

 

Number 

Articles Title

Abstract

1

Non-Minimal Coupling Effects of the Ultra-Light Particles on Photons Velocities in the Radiation Dominated Era of the Universe.

 

El-Nabulsi Ahmad Rami

 

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The effect of the ultra-light masses of the order of the Hubble constant, implemented in Einstein's field equations from non-minimal coupling and supergravities arguments, on photons velocities in the radiation dominated epoch of the Universe within the framework of non-minimal interaction of electromagnetic fields with gravity is developed and discussed in details.

2

A Toy Model of Financial Markets

 

 

J. P. Singh and S. Prabakaran

 

 

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Several techniques of fundamental physics like quantum mechanics, field theory and related tools of non-commutative probability, gauge theory, path integral etc. are being applied for pricing of contemporary financial products and for explaining various phenomena of financial markets like stock price patterns, critical crashes etc.. In this paper, we apply the well entrenched methods of quantum mechanics and quantum field theory to the modeling of the financial markets and the behavior of stock prices. After defining the various constituents of the model including creation & annihilation operators and buying & selling operators for securities, we examine the time evolution of the financial markets and obtain the Hamiltonian for the trading activities of the market. We finally obtain the probability distribution of stock prices in terms of the propagators of the evolution equations.

 

3

Rayleigh process and matrix elements for the one-dimensional harmonic oscillator

 

 

J.H. Caltenco, J.L. López-Bonilla, and J. Morales

 

 

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We show that, the matrix elements <|{e^{-\gamma[x]}|n> for the one-dimensional harmonic oscillator have application in Markov process theory, permitting thus to resolve the Fokker-Planck equation for the two-dimensional probability density corresponding to Rayleigh case.

4

Identical synchronization in chaotic jerk dynamical systems

 

 

Vinod Patidar and K. K. Sud

 

 

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It has been recently investigated that the jerk dynamical systems are the simplest ever systems, which possess variety of dynamical behaviors including chaotic motion. Interestingly, the jerk dynamical systems also describe various phenomena in physics and engineering such as electrical circuits, mechanical oscillators, laser physics, solar wind driven magnetosphere ionosphere (WINDMI) model, damped harmonic oscillator driven by nonlinear memory term, biological systems etc. In many practical situations chaos is undesirable phenomenon, which may lead to irregular operations in physical systems. Thus from a practical point of view, one would like to convert chaotic solutions into periodic limit cycle or fixed point solutions. On the other hand, there has been growing interest to use chaos profitably by synchronizing chaotic systems due to its potential applications in secure communication. In this paper, we have made a thorough investigation of synchronization of identical chaotic jerk dynamical systems by implementing three well-known techniques: (i) Pecora-Carroll (PC) technique, (ii) Feedback (FB) technique and (iii) Active Passive decomposition (APD). We have given a detailed review of these techniques followed by the results of our investigations of identical synchronization of chaos in jerk dynamical systems. The stability of identical synchronization in all the aforesaid methods has also been discussed through the transversal stability analysis. Our extensive numerical calculation results reveal that in PC and FB techniques the x-drive configuration is able to produce the stable identical synchronization in all the chaotic jerk dynamical systems considered by us (except for a few cases), however y-drive and z-drive configurations do not lead to the stable identical synchronization. For the APD approach, we have suggested a generalized active passive decomposition, which leads to the stable identical synchronization without being bothered about the specific form of the jerk dynamical system. Several other active passive decompositions have also been listed with their corresponding conditional Lyapunov exponents to achieve the stable identical synchronization in various chaotic jerk dynamical systems.

 

5

Second Order Perturbation of Heisenberg Hamiltonian for Non-Oriented Ultra-Thin Ferromagnetic Films

 

 

P. Samarasekara

 

 

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The second order perturbation of magnetic energy for ferromagnetic thin films of two and three layers has been studied using classical Heisenberg Hamiltonian. According to our model, the film with two layers is equivalent to an oriented film, when anisotropy constants do not vary inside the film. But the energy of films with three layers indicates periodic variation. Introducing second order perturbation induces some sudden overshooting of energy curves, compared with smooth energy curves obtained for oriented ferromagnetic ultra thin films in one of our previous report. After taking the fourth order anisotropy into account, the overshooting part dominates by reducing the smooth part of energy graphs. Several minimums can be observed in last 3-D graph implying that the film with N=3 can be oriented in some preferred directions by applying a certain value of stress. The shape of graphs of energy variation of all sc(001), fcc(001) and bcc(001) ferromagnetic ultra thin films with second (or fourth) order anisotropy is exactly same. Easy and hard directions of these all types with the effect of second order anisotropy only are 34.4^{0} and 124.4^{0}, respectively. The angle between easy and hard directions is exactly 90^{0} as expected. Although these simulations were given for J/omega =10, D_m^{(2)}/omega =10, K_s /omega =10 and D_m ^{(4)}/omega =5 values only, this same approach can be carried out for any values of J/omega , D_m ^{(2)}/omega ,K_s /omega and D_m ^{(4)}/ omega or any type of ferromagnetic material. Considering the other terms such as dipole interaction and demagnetization factor really complicates the simulation.

 

6

Frameable Processes with Stochastic Dynamics

 

 

Enrico Capobianco

 

 

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A crucial goal in many experimental fields and applications is achieving sparse signal approximations for the unknown signals or functions under investigation. This fact allows to deal with few significant structures for reconstructing signals from noisy measurements or recovering functions from indirect observations. We describe and implement approximation and smoothing procedures for volatility processes that can be represented by frames, particularly wavelet frames, and pursue these goals by using dictionaries of functions with adaptive degree of approximation power. Volatility is unobservable and underlying the realizations of stochastic processes that are non-i.i.d., covariance non-stationary, self-similar and non-Gaussian; thus, its features result successfully detected and its dynamics well approximated only in limited time ranges and for clusters of bounded variability. Both jumps and switching regimes are usually observed though, suggesting that either oversmoothing or de-volatilization may easily occur when using standard and non-adaptive volatility models. Our methodological proposal combines wavelet-based frame decompositions with blind source separation techniques, and uses greedy de-noisers and feature learners.

 

7

Ab-initio Calculations for Forbidden M1/E2 Decay Rates in Ti XIX ion

 

 

A. Farrag

 

 

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The rates of the electric quadrupole E2 and magnetic dipole M1 forbidden transitions in the ground configuration and some excited configurations of the Ti XIX ion have been calculated. The multiconfiguration Hartree - Fock (MCHF) method has been used. The relativistic corrections are included in the Breit-Pauli approximation. A detailed comparison of the present theoretical results with previous calculations and the available data in literature is presented.

8

Some Properties of Generalized Hypergeometric Thermal Coherent States

 

 

Dusan Popov

 

 

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The generalized hypergeometric coherent states (GHCSs) have been introduced by Appl and Schiller [1] In the present paper we have extended some considerations about GHCSs to the mixed (thermal) states and applied, particularly, to the case of pseudoharmonic oscillator (PHO). The Husimi's Q distribution function and the diagonal P - distribution function, in the GHCSs representation, have been deduced for these mixed states. The obtained distribution functions were used to calculate thermal averages and to examine some nonclassical properties of the generalized hypergeometric thermal coherent states (GHTCSs), particularly for the PHO. We have also defined and calculated the thermal analogue of the Mandel parameter and the thermal analogue of the second-order correlation function. By particularizing the parameters p and q of the hypergeometric functions, we recover the usual Barut-Girardello coherent states and their main properties for the PHO from our previous paper [9] All calculations are performed in terms of the Meijer's G-functions [2], which are related to the hypergeometric functions. This manner provides an elegance and uniformity of the obtained results and so the GHCSs become a new field of application for these functions. Moreover, this mathematical approach can be used also for other kind of coherent states (e.g. Klauder-Perelomov, Gazeau-Klauder or nonlinear coherent states ([10] [12]).

 

9

Space-Filling Curves for Quantum Control Parameters

 

 

Fariel Shafee

 

 

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We consider the use of space-filling curves (SFC) in scanning control parameters for quantum chemical systems. First we show that a formally exact SFC must be singular in the control parameters, but a finite discrete generalization can be used with no problem. We then make general observations about the relevance of SFCs in preference to linear scans of the parameters. Finally we present a simple magnetic field example relevant in NMR and show from the calculated autocorrelations that a SFC Peano-Hilbert curve gives a smoother sequence than a linear scan.

 

10

The Spectrum of the Lagrange Velocity Autocorrelation Function in Confined Anisotropic Liquids

 

 

Sakhnenko Elena I and Zatovsky Alexander V.

 

 

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The results of our further analysis of the thermal hydrodynamic fluctuations in an anisotropic liquid under heterogeneous conditions are represented. The heterogeneity is modeled in the form of a plane-parallel layer, the liquid is considered is taken to be incompressible, and the rapid processes of the angular momentum relaxation to equilibrium are ignored. The extended system of hydrodynamics equations is linearized for small deviations from the equilibrium values. For the case of spontaneous fluctuation fields being present in the system of equations for the velocity and inertia tensor components, the boundary problem solution is found in the form of an expansion in the harmonic functions. The spectral densities of the fluctuation correlation functions are obtained by using the fluctuation dissipation theorem (FDT). A special attention is paid to the correlation functions (CFs) for the velocity field in the anisotropic liquid. The spectrum of the Lagrange velocity autocorrelation function (LVACF) and the collective part of the self--diffusion coefficient of the molecules are determined as functions of the coordinate normal to the confining planes.

 

11

On the Quantum Correction of Black Hole Thermodynamics

 

 

Kourosh Nozari and S. Hamid Mehdipour

 

 

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Bekenstein-Hawking Black hole thermodynamics should be corrected to incorporate quantum gravitational effects. Generalized Uncertainty Principle (GUP) provides a perturbational framework to perform such modifications. In this paper we consider the most general form of GUP to find black holes thermodynamics in microcanonical ensemble. Our calculation shows that there is no logarithmic pre-factor in perturbational expansion of entropy. This feature will solve part of controversies in literatures regarding existence or vanishing of this pre-factor.

 

12

A Graphic Representation of States for Quantum Copying

 

 

Sara Felloni and Giuliano Strini

 

 

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The aim of this paper is to introduce a new graphic representation of quantum states by means of a specific application: the analysis of two models of quantum copying machines. The graphic representation by diagrams of states offers a clear and detailed visualization of quantum information's flow during the unitary evolution of not too complex systems. The diagrams of states are exponentially more complex in respect to the standard representation and this clearly illustrates the discrepancy of computational power between quantum and classical systems. After a brief introductive exposure of the general theory, we present a constructive procedure to illustrate the new representation by means of concrete examples. Elementary diagrams of states for single-qubit and two-qubit systems and a simple scheme to represent entangled states are presented. Quantum copying machines as imperfect cloners of quantum states are introduced and the quantum copying machines of Griffiths and Niu and of Buzek and Hillery are analyzed, determining quantum circuits of easier interpretation. The method has indeed shown itself to be extremely successful for the representation of the involved quantum operations and it has allowed to point out the characteristic aspects of the quantum computations examined.

 

 

 

Volume 3, Issue 12 (September 2006)

 

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Number 

Articles Title

Abstract

1

Duality and a Renormalization Scheme for Einsteinian Gravity as a Fix Point Within a Gravitational Gauge Framework

 

Eckehard W. Mielke

 

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A general scheme for a field redefinition (FR) of the coframe and the connection is developed. Within a Yang—Mills type gauge dynamics of gravity, configurations with double dual curvature induced by a \theta-type Chern-Simons terms as generating function reside on an effective Einsteinian background. The effect of the FR on the renormalization and the relation of gravity to effective string models is studied. One encounters a duality of weak and strong couplings of Einsteinian and renormalizable Yang--Mills type gravity as well as an induced cosmological constant of the Anti--de Sitter space.

2

High-Dimensional Dynamics in the Delayed Hénon Map

 

 

J. C. Sprott

 

 

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A variant of the Hénon map is described in which the linear term is replaced by one that involves a much earlier iterate of the map. By varying the time delay, this map can be used to explore the transition from low-dimensional to high-dimensional dynamics in a chaotic system with minimal algebraic complexity, including a detailed comparison of the Kaplan-Yorke and correlation dimensions. The high-dimensional limit exhibits universal features that may characterize a wide range of complex systems including the spawning of multiple coexisting attractors near the onset of chaos.

 

3

Modified Moyal-Weyl Star product in a Curved Non Commutative space-time

 

 

N.Mebarki,F.Khallili , M.Boussahel, and M.Haouchine

 

 

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To generate gravitational terms in a curved noncommutative space-time, new Moyal-Weyl star product as well as Weyl ordering are defined. As an example, a complex scalar mass term action is considered.

4

Light Scattering Studies on the Orientational Behavior of Macromolecular Solutions in a Shear Flow

 

 

J.A. Kupriyanova and A.V. Zatovsky

 

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Theoretical investigation of Rayleigh light scattering by a suspension of anisotropic ellipsoidal particles subjected to a shear flow is carried out. Some properties of the suspension of such particles caused by Brownian rotation of these particles are studied. It is shown that the action of a shear flow induces deformations in the shape of scattering line and results into the non-monotonic frequency dependence of depolarized scattering spectral lines with additional local maxima in the spectra.

 

5

Gödel’s s Geometry: Embedding and Lanczos Spintensor

 

R. García-Olivo, J. López-Bonilla, S. Vidal-Beltrán, SEPI-ESIME-Zacatenco

 

 

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We exhibit an open problem: To investigate if the Gödel's metric accepts local and isometric embedding into E_6. Besides, we show that in this metric there is a symmetric tensor which generates algebraically to Riemann tensor and differentially to Weyl tensor.

 

6

Thermopower of The Quantum Point Contacts Under the Effects of Boundary Roughness

 

 

Attia A. Awad Alla

 

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In this paper we, study the influence of scattering by boundary roughness on electron transport through quantum point contact. It is found that the thermo power of rough quantum point contact shows random and rapid fluctuations and strong with variable the Fermi energy and electrochemical potential. The thermoelectric efficiency as function of electrochemical potential and the oscillations are periodic and even in the electrochemical potential. These results agree with existing experiments and can be used as a guideline for the evaluation of the fabrication process of quantum point contact.

 

7

Matrix Theory and the Modified Space-Time Uncertainty

 

Abbas Farmany

 

 

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We consider the modified space-time uncertainty in the matrix theory point of view. First, we find a suitable theorem for the modified space-time uncertainty. Furthermore, this theorem is proved in the matrix theory compactifications.

8

Analytical One-Photon Double Differential Spectrum From In-Flight Decay of Scalar Neutral Mesons

 

 

Giuseppe Russo and Antonio Giusa

 

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We introduce a direct simple method to evaluate the one-photon double differential spectrum from the decay of pseudo-scalar neutral mesons. The analytical distributions of the opening angle and of the ratio of energies of the two gammas are then straightforwardly deduced. The physical interest is also outlined.

 

9

On the Finite Caputo and Finite Riesz Derivatives

 

 

A. M. A. El-Sayed and M. Gaber

 

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In this paper, we give some properties of the left and right finite Caputo derivatives. Such derivatives lead to finite Riesz type fractional derivative, which could be considered as the fractional power of the Laplacian operator modelling the dynamics of many anomalous phenomena in super-diffusive processes. Finally, the exact solutions of certain fractional diffusion partial differential equations are obtained by using the Adomain decomposition method and some new diffusion-wave equations are presented.

 

10

Numerical Classical and Quantum Mechanical Simulations of Charge Density Wave Models

 

 

A. W. Beckwith

 

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First, using a driven harmonic oscillator model by a numerical scheme formulated by Littlewood, we present a computer simulation of charge density waves (CDW); next, we use this simulation to show how the dielectric model presented via this procedure leads to a blow up at the initialization of a threshold field E_T. Finding this approach highly unphysical, we initiated inquiry into alternative models. We investigate how to present the transport problem of CDW quantum mechanically, through a numerical simulation of the massive Schwinger model. We find that this single-chain quantum mechanical simulation used to formulate solutions to CDW transport is insufficient for transport of soliton-antisolitons (S-S') through a pinning gap model of CDW. We show that a model Hamiltonian with Peierls condensation energy used to couple adjacent chains (or transverse wave vectors) permits formation of S-S' that can be used to transport CDW through a potential barrier. This addition of the Peierls condensation energy term is essential for any quantum model of CDW to give a numerical simulation to tunneling behavior.

 

11

A New Wave Quantum Relativistic Equation from Quaternionic Representation of Maxwell-Dirac Isomorphism as an Alternative to Barut-Dirac Equation

 

 

V. Christianto

 

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It is known that Barut's equation could predict lepton and hadron mass with remarkable precision. Recently some authors have extended this equation, resulting in Barut-Dirac equation. In the present article we argue that it is possible to derive a new wave equation as alternative to Barut-Dirac's equation from the known exact correspondence (isomorphism) between Dirac equation and Maxwell electromagnetic equations via biquaternionic representation. Furthermore, in the present note we submit the viewpoint that it would be more conceivable if we interpret the vierbein of this equation in terms of superfluid velocity, which in turn brings us to the notion of topological electronic liquid. Some implications of this proposition include quantization of celestial systems. We also argue that it is possible to find some signatures of Bose-Einstein cosmology, which thus far is not explored sufficiently in the literature. Further experimental observation to verify or refute this proposition is recommended.

 

12

A Dynamics of Charged Spherically Symmetric Thick Shell

 

 

A. Eid

 

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We Consider a spherically symmetric thick shell in two different space times. We have used the equation of motion for thick shell, developed by Khakshournia and Mansouri, to obtain the equation of motion of a charged spherical shell. We Expand the dynamical equation of motion of thick shell, to the first order of its thickness, to compare it with the dynamics of charged thin shell. It is shown that the effect of thickness is to speed up the collapse of the shell.

 

 

 

Volume 3, Issue 13 (December 2006)

 

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Number 

Articles Title

Abstract

1

Particle Interference without Waves

 

 

Marcello Cini

 

 

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After eighty years of Quantum Mechanics (QM) we have learned to live with wave functions without worrying about their physical nature. This attitude is certainly justified by the extraordinary success of the theory in predicting and explaining not only all the phenomena encountered in the domain of microphysics, but also some spectacular nonclassical macroscopic behaviors of matter. Nevertheless one cannot ignore that the wave--particle duality of quantum objects not only still raises conceptual problems among the members of the small community of physicists who are still interested in the foundations of our basic theory of matter, but also induces thousands and thousands of physics students all around the world to ask each year, at their first impact with Quantum Mechanics, embarrassing questions to their teachers without receiving really convincing answers. Remember that Feynman once said ``It is fair to say that nobody understands Quantum Mechanics''. My purpose is to show that these difficulties can only be faced by pursuing a line of research which takes for granted the irreducible nature of randomness in the quantum world. This can be done by eliminating from the beginning the unphysical concept of wave function. I believe that this elimination is conceptually similar to the elimination of the aether, together with its paradoxical properties, from classical electrodynamics, accomplished by relativity theory. In our case the lesson sounds: No wave functions, no problems about their physical nature. Furthermore, the adoption of a statistical approach from the beginning for the description of the physical properties of quantum systems sounds methodologically better founded than the conventional ad hoc hybrid procedure of starting with the determination of a system's wave function of unspecified nature followed by a ``hand made'' construction of the probability distributions of its .physical variables.

2

Metric Variation Inside Transitioning Superconducting Shells

 

 

J. R. Claycomb and R. M. Chu

 

 

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In this paper, we outline the forward problem of metrical variation due to the Casimir effect in transitioning superconducting shells. We consider a massless scalar quantum field inside a hollow superconducting sphere and a cylinder. Metric equations are developed describing the evolution of the scale factors after the superconducting shells transition to the normal state.

 

3

Black Scholes Option Pricing with Stochastic Returns on Hedge Portfolio

 

 

J. P. Singh and S. Prabakaran

 

 

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The Black Scholes model of option pricing constitutes the cornerstone of contemporary valuation theory. However, the model presupposes the existence of several unrealistic and rigid assumptions including, in particular, the constancy of the return on the ``hedge portfolio''. There, now, subsists ample justification to the effect that this is not the case. Consequently, several generalisations of the basic model have been attempted. In this paper, we attempt one such generalisation based on the assumption that the return process on the ``hedge portfolio'' follows a stochastic process similar to the Vasicek model of short-term interest rates.

4

Co-Existence of Regular and Chaotic Motions in the Gaussian Map

 

 

Vinod Patidar

 

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In this communication, the Gaussisn map, which has drawn less attention in the past as compare to other one-dimensional maps, has been explored. Particularly, the dynamical behavior of the Gaussian map and the presence of co-existing attractors (which is a rare phenomenon in one-dimensional maps) in the complete parameter space have been investigated. We also suggest a possible geometrical reason for the emergence of co-existing attractors at a particular set of system parameters, which works for all one-dimensional maps. The regions of parameter space, where regular and chaotic motions co-exist, have also been identified.

 

5

Does the Formation of Temperature Dependence of Axion Walls Help Delineate a Regime Where the Wheeler De Witt Equation Holds?

 

A. W. Beckwith

 

 

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We examine from first principles the implications of the 5^{th} Randall Sundrum Brane world dimension in terms of setting initial conditions for chaotic inflationary physics. Our model pre supposes that the inflationary potential pioneered by Guth is equivalent in magnitude in its initial inflationary state to the effective potential presented in the Randall -Sundrum model We also consider an axion contribution to chaotic inflation (which may have a temperature dependence) which partly fades out up to the point of chaotic inflation being matched to a Randall -- Sundrum effective potential. If we reject an explicit axion mass drop off to infinitesimal values at high temperatures, we may use the Bogomolnyi inequality to re scale and re set initial conditions for the chaotic inflationary potential. Then the Randall-Sundrum brane world effective potential delineates the end of the dominant role of di quarks, and the beginning of inflation. It also leads to a new region where the Wheeler De Witt equation

holds.

 

6

Extended Non Symmetric Gravitation Theory with a Scalar Field in Non Commutative Geometry

 

 

N.Mebarki, F.Khelili and J.Mimouni

 

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An extended method to reformulate the non symmetric gravitation theory in the non commutative geometry formalism is presented where all the lagrangian terms, including the various interaction ones with scalar fields, emerge naturally.

 

7

Some Important Features of Ultra-Light Particles, Induced Cosmological Constant and Massive Gravitons in Modern Cosmology Theories

 

El-Nabulsi Ahmad-Rami

 

 

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Some important features of ultra-light masses and induced cosmological constant implemented in Einstein gravity theory from supergravities arguments and non-minimal coupling effects are presented and discussed in some details in modern cosmology where massive gravitons are taken into account.

8

Building of Heat Kernel on Non-CompactHomogeneous Spaces

 

 

V. Mikheyev and I. Shirokov

 

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Method of the solution of the main problem of homogeneous spaces thermodynamics on non-compact spaces in the case of non-compact homogeneous spaces is presented in the article. The method is based on the formalism of coadjoint orbits. In that article we present algorithm that allows efficiently evaluate heat kernel on non-compact homogeneous spaces. The method is illustrated with non-trivial example.

 

9

Radiating Shell Supported by a Phantom Energy

 

 

A. Eid

 

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I describe the evolution of a thin spherically symmetric self-gravitating phantom shell around the radiating shell. The general equations describing the motion of shell with a general form of equation of state are derived. The stability analysis of this phantom shell to linearized spherically symmetric perturbation about static equilibrium solution is carried out.

 

10

Radial Matrix Elements for the Hydrogen Atom

 

 

M. Enciso-Aguilar, J. López-Bonilla and M. S'anchez-Meraz

 

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It is known that the hydrogenlike atom can be studied as a Morse oscillator, then here we show that these fact leads to an interesting method to obtain the matrix elements for the Coulomb potential.

 

11

A Simply Regularized Derivation of the Casimir Force

 

 

H. Razmi

 

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We want to calculate the Casimir force between two parallel, uncharged, perfectly conducting plates by a simple automatically regularized approach. Although in the well-known methods one should explicitly subtract the energy term due to the empty space to regularize the calculation, here, the regularization is simply/implicitly achieved by considering only the energy per unit area of each plate.

 

 

Volume 4, Issue 14 (March 2007)

 

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Number 

Articles Title

Abstract

1

On the Dynamics of a n-D Piecewise Linear Map

 

Zeraoulia Elhadj

 

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This paper, derives sufficient conditions for the existence of chaotic attractors in a general n-D piecewise linear discrete map, along the exact determination of its dynamics using the standard definition of the largest Lyapunov exponent.

2

Flow of Unsteady Dusty Fluid Under Varying Pulsatile Pressure Gradient in Anholonomic Co-ordinate System

 

B.J.Gireesha, C.S.Bagewadi and B.C.Prasanna

Kumara

 

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An analytical study of unsteady viscous dusty fluid flow with uniform distribution of dust particles between two infinite parallel plates has been studied by taking into the account of the influence of pulsatile pressure gradient. The flow analysis is carried out using differential geometry techniques and analytical solutions of the problem is obtained with the help of Laplace Transform technique and which are discussed with the help of graphs.

 

3

Exact Solutions for Nonlinear Evolution Equations Via Extended Projective Riccati Equation Expansion Method

 

M A Abdou

 

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By means of a simple transformation, we have shown that the generalized-Zakharov equations, the coupled nonlinear Klein-Gordon-Zakarov equations, the GDS, DS and GZ equations and generalized Hirota-Satsuma coupled KdV system can be reduced to the elliptic-like equations. Then, the extended projective Riccati equation expansion method is used to obtain a series of solutions including new solitary wave solutions,periodic and rational solutions. The method is straightforward and concise, and its applications is promising.

4

Evolutionary Neural Gas (ENG) : A Model of Self Organizing Network from Input Categorization

 

I. Licata and L. Lella

 

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Despite their claimed biological plausibility, most self organizing networks have strict topological constraints and consequently they cannot take into account a wide range of external stimuli. Furthermore their evolution is conditioned by deterministic laws which often are not correlated with the structural parameters and the global status of the network, as it should happen in a real biological system. In nature the environmental inputs are noise affected and ``fuzzy''. Which thing sets the problem to investigate the possibility of emergent behaviour in a not strictly constrained net and subjected to different inputs. It is here presented a new model of Evolutionary Neural Gas (ENG) with any topological constraints, trained by probabilistic laws depending on the local distortion errors and the network dimension. The network is considered as a population of nodes that coexist in an ecosystem sharing local and global resources. Those particular features allow the network to quickly adapt to the environment, according to its dimensions. The ENG model analysis shows that the net evolves as a scale-free graph, and justifies in a deeply physical sense- the term ``gas'' here used.

5

Discrete Groups Approach to Non Symmetric Gravitation Theory

 

N.Mebarki, F.Khelili and J.Mimouni

 

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A generalized discrete group formalism is obtained and used to describe the Non Symmetric Gravity theory (NGT) coupled to a scalar field. We are able to derive explicitly the various terms of the NGT action including the interaction term without any ad-hoc assumptions.

6

Quantization of the Scalar Field Coupled Minimally to the Vector Potential

 

W. I. Eshraim and N. I. Farahat

 

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A system of the scalar field coupled minimally to the vector potential is quantized by using canonical path integral formulation based on Hamilton-Jacobi treatment. The equation of motions are obtained as total differential equation and the integrability conditions are examined.

7

A Generalized Option Pricing Model

 

J. P. Singh

 

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The Black Scholes model of option pricing constitutes the cornerstone of contemporary valuation theory. However, the model presupposes the existence of several unrealistic assumptions including the lognormal distribution of stock market price processes. There, now, subsists abundant empirical evidence that this is not the case. Consequently, several generalisations of the basic model have been attempted with relaxation of some of the underlying assumptions. In this paper, we postulate a generalization that contemplates a statistical feedback process for the stochastic term in the Black Scholes partial differential equation. Several interesting implications of this modification emanate from the analysis and are explored.

8

Derivation of the Radiative Transfer Equation Inside a Moving Semi-Transparent Medium of Non Unit Refractive Index

 

V. LE DEZ and H. SADAT

 

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The derivation of the radiative transfer equation inside a moving semi-transparent medium of non unit constant refractive index has been completely achieved, leading to an exactly similar equation as in the case of a unit index, unless it is expressed in a particular frame with particular time and space co-ordinates; defining first the ``equivalent vacuum'' and the ``matter'' space associated to its ``matter'' co-ordinates with the help of the Gordon's metric, it is shown that an observer at rest in vacuum perceives the isotropic moving medium as an anisotropic uniaxial medium of given optical axis, for which it is possible to derive general transmission and reflection rules for electromagnetic fields; however the exhibited refractive index characterising the moving medium, relatively to the observer located in vacuum, is not an effective index but only an apparent one without any energetic significance, and the specific intensity must be obtained relatively to a given observer at rest located inside the moving medium; finally the general form of the radiative transfer equation is obtained in the moving medium.

9

Quantum Images and the Measurement Process

 

Fariel Shafee

 

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We argue that symmetrization of an incoming microstate with similar states in a sea of microstates contained in a macroscopic detector can produce an effective image, which does not contradict the no-cloning theorem, and such a combinatorial set, with conjugate quantum numbers can form virtual bound states with the incoming microstate. This can then be used with first passage random walk interactions to give the right quantum mechanical weight for different measured eigenvalues.

 

Volume 4, Issue 15 (July 2007)

 

Full text: Acrobat PDF (1,725 KB)

 

Number 

Articles Title

Abstract

1

Mental and Physical Objects in Quantum Mechanics:Any Lessons for Other Disciplines?

 

 

M. Cini

 

 

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The standard formulation of Quantum Mechanics has raised from its beginning animated discussions about the interpretation of the counterintuitive properties of mental objects (wave functions or Schrödinger waves) introduced to represent the properties of the physical objects. Two questions have since then been formulated to which a universally accepted answer is still lacking. The first one (Bohr, von Neumann) concerns the ontological nature of physical reality (the existence of classical objects) and the role of the observer (wave packet collapse) in assessing it. The second one is the non local character of quantum physical quantities (Einstein Podolski Rosen [EPR] long distance correlation of particles). An alternative formulation of Quantum Mechanics, originally proposed in 1932 by Eugene Wigner, taken up by Richard Feynman in 1987, and reelaborated by myself in the years from 1998 to 2003, is possible. The mental objects of standard Quantum Mechanics (Schrödinger waves) no longer appear in this new formulation and are replaced by new ones (Wigner functions) which do not show any more the puzzling properties which worried Einstein. My conclusion from the preceding discussion is that different explanations of a given set of experimental data may be derived according to the different nature of the mental objects introduced to represent the properties of the physical objects involved. The confusion between these two kind of objects may be, however, very misleading. I will finally discuss two examples of this conclusion from Biology and Economics.

2

Fantappié-Arcidiacono Theory of Relativity Versus Recent Cosmological Evidences : A Preliminary Comparison

 

 

L. Chiatti

 

 

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Notwithstanding the Fantappié -Arcidiacono theory of projective relativity was introduced more than half a century ago, its observational confirmations in cosmology (the only research field where its predictions differ from those of the Einsteinian relativity) are still missing. In line of principle, this theory may be proposed as a valid alternative to the current views assuming the dominance of dark matter and inflationary scenarios. In this work, the relativistic transformation of the Poynting vector associated with the reception of electromagnetic waves emitted by astronomical objects is derived in the context of the special version of the theory. On the basis of this result, and some heuristic assumptions, two recent collections of observational data are analyzed : the m-z relation for type Ia supernovae (SNLS, SCP collaborations) and the log N -- log S relation obtained from the FIRST survey of radio sources at 1.4 GHz. From the first analysis, values are derived for the current density of matter in the universe and the cosmological constant that are of the same order of magnitude as those obtained from the most recent conventional evaluations. The second analysis results in an evolutionary trend of number of sources as a function of z that is in qualitative agreement with that obtained from more conventional analyses. Therefore it can be concluded, as a preliminary result, that the application of the theory to the study of cosmological processes leads to results which not substantially differ from these currently accepted. However, in order to obtain a more reliable comparison with observations, a solution is needed for the gravitational equations in the general version of the theory.

3

Considering Relativistic Symmetry as the First Principle of Quantum Mechanics

 

 

T. Kawahara

 

 

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On the basis of the relativistic symmetry of Minkowski space, we derive a Lorentz invariant equation for a spread electron. This equation slightly differs from the Dirac equation and includes additional terms originating from the spread of an electron. Further, we calculate the anomalous magnetic moment based on these terms. These calculations do not include any divergence; therefore, renormalization procedures are unnecessary. In addition, the relativistic symmetry existing among coordinate systems will provide a new prospect for the foundations of quantum mechanics like the measurement process.

4

On Certain Quantization Aspects of (Generalized) Toda Systems

 

 

M. Legare

 

 

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Ordinary and gl(n,\R) generalized Toda systems as well as a related hierarchy are probed with respect to certain quantization characteristics. ``Quantum" canonical and Poisson transformations are used to study quantizations of transformed Toda systems. With a Lax pair setting, a hierarchy of related systems are shown and their quantizations discussed. Finally, comments are added about quantum aspects of gl(n,\R) generalized Toda systems with the approaches of deformation quantization or quantum groups in mind.

5

Klein -Gordon Equation for the Heating of the Fermionic Gases

 

 

M.Pelc, J. Marciak - Kozlowska and M. Kozlowski

 

 

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In this paper the model for the interaction of the ultra-short laser pulses with matter is proposed. The Klein-Gordon equation for heat transport is developed and solved. The condition for the existence of the massless heat carriers is formulated. The condition is V\tau =\hbar /8, where V is potential energy, \tau is the relaxation time. The new thermal Klein-Gordon equation can be applied to the study of thermal processes for the fermionic gases (electron, nucleon).

6

Deformation Quantization of Submanifolds and Reductions via Duflo-Kirillov-Kontsevich Map

 

 

A. Chervov and L. Rybnikov

 

 

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We propose the following recipe to obtain the quantization of the Poisson submanifold $N$ defined by the equations f_i=0 (where f_i are Casimirs) from the known quantization of the manifold M: one should consider factor algebra of the quantized functions on M by the images of D(f_i), where D: Fun(M) \to Fun(M)\otimes \CC[\hbar] is Duflo-Kirillov-Kontsevich map. We conjecture that this algebra is isomorphic to quantization of Fun(N) with Poisson structure inherited from M. Analogous conjecture concerning the Hamiltonian reduction saying that "deformation quantization commutes with reduction" is presented. The conjectures are checked in the case of S^2 which can be quantized as a submanifold, as a reduction and using recently found explicit star product. It's shown that all the constructions coincide.

7

Hidden Symmetry, Excitonic Transitions and Two-Dimensional Kane's Exciton in the Quantum Well

 

 

E.M. Kazaryan, L.S. Petrosyan, and H.A. Sarkisyan

 

 

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The influence of hidden symmetry on two-dimensional excitonic states in semiconductor quantum wells is investigated. It is shown that excitonic states in quantum wells, with the parabolic dispersion law for the electron and hole, and Sommerfeld's coefficients for excitonic transitions are determined only with the principle quantum number within the framework of two-dimensional Coulomb potential. This is a result of hidden symmetry of two-dimensional Coulomb problem, conditioned by the existence of two-dimensional analog of the Runge-Lentz vector. For the narrow gap semiconductor quantum well with the non-parabolic dispersion law of electron and hole, in the two-band Kane model, it is shown that two-dimensional excitonic states are described in the frames of analog of the Klein-Gordon equation with the two-dimensional Coulomb potential. Non-stability of the ground state of the two-dimensional Kane's exciton investigated.

8

Debever-Penrose Principal Directions in Terms of Null Canonical Vectors

 

 

N. Hamdan, R. Garcia-Olivo, and J. Lopez-Bonilla

 

 

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We show explicit expressions to construct the Debever-Penrose vectors from a given null canonical tetrad.

9

How Can Brane World Physics Influence Axion Temperature Dependence, Initial Vacuum States, and Permissible Solutions to the Wheeler-De Witt Equation in Early Universe Cosmology?

 

 

A.W. Beckwith

 

 

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We use an explicit Randall-Sundrum brane world effective potential as congruent with conditions needed to form a minimum entropy starting point for an early universe vacuum state. We are investigating if the Jeans instability criteria mandating low entropy, low temperature initial pre inflation state configuration can be reconciled with thermal conditions of temperatures at or above ten to the 12 Kelvin, or higher, when cosmic inflation physics takes over. We justify this by pointing to the Ashtekar, Pawlowski, and Singh (2006) article about a prior universe being modeled via their quantum bounce hypothesis which states that this prior universe geometrically can be modeled via a discretized Wheeler -- De Witt equation , with it being the collapsing into a quantum bounce point singularity converse of the present day universe expanding from the quantum bounce point so delineated in their calculations. The prior universe would provide thermal excitation into the Jeans instability mandated cooled down initial state, with low entropy, leading to extreme graviton production. This necessitates reconciling the lack of a quantum bounce seen in brane world models with the proof of relic graviton production so provided in the simulation so provided. This is also a way of getting around the get around the fact that conventional cosmological CMB is limited by a barrier as of a red shift limit of about z = 1000, i.e. when the universe was about 1000 times smaller and 100,000 times younger than today as to photons, and to come up with a working model of quintessence scalar fields which permits relic generation of dark matter/dark energy.

10

Gravitation and Gauge Fields in a Space with 4+n Dimensions

 

 

Ion Rosu

 

 

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In this paper, for a particular symmetry, we obtain the geodesics' and field equations in a space with 4+n dimensions. The geodesics equations represent the motion equations in the presence of gravitation field and gauge fields. All fields depend of x=\left\{ {x^\alpha } \right\}\in M^4 and do not depend of y=\left\{ {y^k} \right\}\in M^n. The field equations are Einstein equations in a space with 4+n dimensions. The gravitation field is represented by the tensor components G_{\alpha \beta } which satisfy nonlinear equations in M^4. If M^4 is a subspace in a space with 4+n_g dimensions, then G_{\alpha \beta } =G_{\alpha \beta }^0 +g_\alpha ^{r_0 } g_{\beta r_0 } and in this space the fields g_\alpha ^{r_0 } satisfy the same type of equations satisfied by the gauge fields g_\alpha ^{r } . This allows the quantification of gravitation fields $g_\alpha ^{r_0 }.

11

Fractional Path Integral and Exotic Vacuum for the Free Spinor Field Theory with Grassman Anticommuting Variables

 

 

EL-NABULSI Ahmad Rami

 

 

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A systematic formulation of fractional path integral for the free spinor field theory is presented and discussed within the framework of fractional action-like variational approach (or fractionally differentiated Lagrangian function) recently formulated by the author. Some interesting explicit formulas and features are discussed in some details.

12

Randomized Time and Frequency Domain Estimation from Semimartingales

 

 

Enrico Capobianco

 

 

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One established fact in financial economics and mathematics is the convergence of realised to integrated volatility according to the quadratic variation principle. When computed in general semimartingale asset price models, the cumulative squared high frequency returns represent consistent estimators of the integrated volatility. Both time and frequency domain estimators are available for solving what, in an unifying approach, could be considered an inverse problem, the recovery of latent volatility from the realizations of observable return processes. Since the relation between realised and integrated volatility implies that one is transformed into the other with noise, we work in a simulated environment of Brownian motion paths for exemplifying the semimartingale context and produce randomized estimators for the volatility. With the support of experimental evidence, we can show the consistency of time- and frequency-based volatility estimators and their speed of convergence to the quadratic variation limit.

12

Microwave Induced Tunneling in Stub Tuner Mesoscopic Device and its Chaotic Behavior

 

 

Attia A. AwadAlla, Arafa H. Aly, and Adel H. Phillips

 

 

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We study the thermoelectric transport properties of mesoscopic devices in which the dynamics of the electrons are chaotic. The present studied device is an electronic stub tuner modeled as S-Sm-S-Sm-S (S-superconductor, Sm-semiconductor). The thermo power of the present device is expressed in terms of the conductance of the system, which is derived by the technique based on Landauer-Buttiker equation. The influence of time-varying fields on the transport through such device has been taken into consideration and also the effect of magnetic field. The results show an oscillatory behavior of the dependence of the thermo power on both the magnetic field and frequency of the induced field. These oscillations appear as random fluctuation in peak heights. Analysis of these results shows that mesoscopic fluctuations obey Lorentzian distribution and under some conditions it is an exponential distribution. Our results are found concordant with those in the literature.

 

Classical Heisenberg Hamiltonian Solution of Oriented Spinel Ferrimagnetic Thin Films

 

 

P. Samarasekara

 

 

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The classical Heisenberg Hamiltonian was solved for oriented spinel thin and thick cubic ferrites. The dipole matrix of complicated cubic cell could be simplified into the form of dipole Matrix of simple cubic cells. This study was confined only to the highly oriented thin films of ferrite. The variation of total energy of Nickel ferrite thin films with angle and number of layers was investigated. Also the change of energy with stress induced anisotropy for Nickel ferrite films with N=5 and 1000 has been studied. Films with the magnetic moments ratio 1.86 can be easily oriented in \theta =90^{0} direction when Nis greater than 400. Although this simulation was performed only for \frac{J}{\omega }=100,\frac{\sum\limits_{m=1}^N D_m ^{(\ref{eq2})}}{\omega }=10,\frac{H_{in} }{\omega }=\frac{H_{out} }{\omega }=0,\frac{K_s }{\omega }=5 \mbox{ and } \frac{\sum\limits_{m=1}^N D_m ^{(4)}}{\omega }=5 as an example, these equations can be applied for any value of \frac{J}{\omega },\frac{\sum\limits_{m=1}^N D_m ^{(\ref{eq2})}}{\omega },\frac{H_{in} }{\omega },\frac{H_{out} }{\omega },\frac{K_s }{\omega } \, \mbox{ and } \, \frac{\sum\limits_{m=1}^N D_m

^{(4)}}{\omega }.

Volume 4, Issue 16 III (December 2007)

 

Full text: Acrobat PDF (763 KB)

 

Number 

Articles Title

Abstract

1

Multiboundary Algebra as Pregeometry

 

 

Ben Goertzel

 

 

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It is well known that the Clifford Algebras, and their quaternionic and octonionic subalgebras, are structures of fundamental importance in modern physics. ~Geoffrey Dixon has even used them as the centerpiece of a novel approach to Grand Unification. ~ In the spirit of Wheeler's notion of "pregeometry" and more recent work on quantum set theory, the goal of the present investigation is to explore how these algebras may be seen to emerge from a simpler and more primitive order. In order to observe this emergence in the most natural way, a pregeometric domain is proposed that consists of two different kinds of boundaries, each imposing different properties on the combinatory operations occurring between elements they contain. ~It is shown that a very simple variant of this kind of "multiboundary algebra" gives rise to Clifford Algebra, in much the same way as Spencer-Brown's simpler single-boundary algebra gives rise to Boolean algebra.

2

Scale Relativity: A Fractal Matrix for Organization in Nature

 

 

Laurent Nottale

 

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In this review paper, we recall the successive steps that we have followed in the construction of the theory of scale relativity. The aim of this theory is to derive the physical behavior of a nondifferentiable and fractal space-time and of its geodesics (to which wave-particles are identified), under the constraint of the principle of relativity of all scales in nature. The first step of this construction consists in deriving the fundamental laws of scale dependence (that describe the internal structures of the fractal geodesics) in terms of solutions of differential equations acting in the scale space. Various levels of these scale laws are considered, from the simplest scale invariant laws to the log-Lorentzian laws of special scale relativity. The second step consists in studying the effects of these internal fractal structures on the laws of motion. We find that their main consequence is the transformation of classical mechanics in a quantum-type mechanics. The basic quantum tools (complex, spinor and bi-spinor wave functions) naturally emerge in this approach as consequences of the nondifferentiability. Then the equations satisfied by these wave functions (which may themselves be fractal and nondifferentiable), namely, the Schrödinger, Klein-Gordon, Pauli and Dirac equations, are successively derived as integrals of the geodesics equations of a fractal space-time. Moreover, the Born and von Neumann postulates can be established in this framework. The third step consists in addressing the general scale relativity problem, namely, the emergence of fields as manifestations of the fractal geometry (which generalizes Einstein's identification of the gravitational field with the manifestations of the curved geometry). We recall that gauge transformations can be identified with transformations of the internal scale variables in a fractal space-time, allowing a geometric definition of the charges as conservative quantities issued from the symmetries of the underlying scale space, and a geometric construction of Abelian and non-Abelian gauge fields. All these steps are briefly illustrated by examples of application of the theory to various sciences, including the validation of some of its predictions, in particular in the domains of high energy physics, sciences of life and astrophysics.

 

Volume 5, Issue 17 (March 2008)

 

Full text: Acrobat PDF (3,010 KB)

 

 

Number 

Articles Title

Abstract

1

A Review of Leading Quantum Gravitational Corrections to Newtonian Gravity

 

Arif Akhundov and Anwar Shiekh

 

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In this review we present the theoretical background for treating General Relativity as an effective field theory and focus on the concrete results of such a treatment. As a result we present the calculations of the low-energy leading gravitational corrections to the Newtonian potential between two sources.

 

2

Radiation Reaction at Extreme Intensity

Richard T. Hammond

 

 

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The radiation reaction force is examined for an idealized short pulse of electromagnetic radiation and for a plane wave. Exact solutions (without radiation reaction) are discussed, the total radiated power is calculated. A new and simpler approach to the approximate form of the equation of motion is presented that automatically removes the runaway solutions. Finally, analytical solutions are presented for the equations of motion that include the radiation reaction forces in the very high intensity regime. A classical scattering angle is defined and it shows that the electron is scattered in a small cone in the forward direction. The radiation reaction corrections to this angle are also considered.

3

Super-Light Electromagnetic Wave With Longitudinal And Transversal Modes

 

M.M. Kononenko

 

 

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The transformation converting equations invariant under Lorentz into the equations invariant under Galileo is obtained. On this basis:(1) the super-light electromagnetic wave with longitudinal and transversal modes is found out; (2) it is shown the wave velocity coincides with that of de Broglie's wave; (3) the connection between Maxwell's electrodynamics and Shr\"{o}dinger's equation is established; (4) structural elements of space are discovered and ``a horizon of visibility'' is found. It is shown Bell's inequalities and the principle of the light speed constancy are based on the SRT artifact and ``Einstein's local realism'' is determined by the wave referred above. Objectivity of results for quantum and classical objects is discussed.

4

Non Commutative Geometry Constraints and the Standard Renormalization Group Approach: Two Doublets Higgs Model as An Example.

 

N.Mebarki and M.Harrat

 

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The Chamssedine-Fr\"{o}hlich Approach to Noncommutative Geometry (NCG) is extended and applied to the reformulation of the two doublets Higgs model. The Fuzzy mass, coupling and unitarity relations are derived. It is shown that the latter are no more preserved under the renormalization group equations obtained from the standard quantization method. This suggests to look for an appropriate NCG quantization procedure.

5

Hamilton-Jacobi Formulation of a Non-Abelian Yang-Mills Theories

 

W. I. Eshraim and N. I. Farahat

 

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A non-Abelian theory of fermions interacting with gauge bosons is treated as a constrained system using the Hamilton-Jacobi approach. The equations of motion are obtained as total differential equations in many variables. The integability conditions are satisfied, and the set of equations of motion is integrable. A comparison with Dirac's method is done

6

Physical Form of The Clustering Parameter And Gravitational Galaxy Clustering

 

Sajad Masood , Manzoor A Malik, Shakeel Ahmad and N. A. Rather

 

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A theory for a system clustering under gravity is developed for the clustering parameter b(n,T), in terms of a partial differential equation using thermodynamic technique. Various solutions of the differential equation relate b(n,T) with density n and temperature T of the gravitating system. The physical validity of various solutions of b(n,T) on the basis of certain boundary conditions and probability density distribution function is discussed. Results indicate that the clustering parameter depends on the specific combination nT^{-3}. The theory also provides a new insight into gravitational clustering.

7

Penrose Model Potential, Compared With Coleman- Weinberg Potential for Early Universe Scalar Evolution

A.W. Beckwith

 

 

 

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We present evidence in terms of a D'Alembertain operator acting on a scalar field minus the first derivative of a potential system, with respect to an inflaton scalar field, that the Penrose model as outlined as an alternative to cosmological big crunch models gives us emergent behavior for an inflaton scalar field in early universe cosmological models. This is in contrast to the Coleman-Weinberg potential which in low temperature conditions is always presenting almost non existent emergent scalar fields. This permits us to state that Penrose's cyclic universe model in its initial conditions gives us scalar field dynamics consistent with emergent scalar fields which die out quickly as temperature drops after the onset of inflation. We make no attempt to find the particulars of the conformal mapping which allows the alternative to the big crunch Penrose (2007) lectured upon in the inaugural meeting of the IGC at Penn State.

8

Increasing Effective Gravitational Constant In Fractional Add Brane Cosmology

 

El-Nabulsi Ahmad Rami

 

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Arkani--Hamed--Dimopoulos--Dvali brane model with time--increasing scaling gravitational constant is constructed within the framework of fractional action--like variational approach with one positive parameter `\alpha'.

9

A Two-Dimensional Discrete Mapping with C^{Infinity} Multifold Chaotic Attractors

 

Zeraoulia Elhadj and J. C. Sprott

 

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This paper introduces a two-dimensional, C^{\infinity} discrete bounded map capable of generating "multi- fold" strange attractors via period-doubling bifurcation routes to chaos.

10

Bosons-Parafermions Wess-Zumino Model

 

L. Maghlaoui and N. Belaloui

 

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A Wess-Zumino model in terms of bosons and parafermions of order p=2 is investigated.\,We show that the parasupercharges associated to the parasupersymmetric transformations satisfy the p=2 trilinear relations. The closure of the transformations algebra is established with a trilinear product rule for the fermionic elements. Finally, we verify that these parasupercharges are really the generators of the parasupersymmetric transformations.

11

Geometrodynamics of Information on Curved Statistical Manifolds and Its Applications to Chaos

 

C. Cafaro and S. A. Ali

 

 

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A novel information-geometrodynamical approach to chaotic dynamics (IGAC) on curved statistical manifolds based on Entropic Dynamics (ED) is presented and a new definition of information geometrodynamical entropy (IGE) as a measure of chaoticity is proposed. The general classical formalism is illustrated in a relatively simple example. It is shown that the hyperbolicity of a non-maximally symmetric 6N-dimensional statistical manifold {M}_{s} underlying an ED Gaussian model describing an arbitrary system of 3N degrees of freedom leads to linear information-geometric entropy growth and to exponential divergence of the Jacobi vector field intensity, quantum and classical features of chaos respectively. An information-geometric analogue of the Zurek-Paz quantum chaos criterion in the classical reversible limit is proposed. This analogy is illustrated applying the IGAC to a set of n-uncoupled three-dimensional anisotropic inverted harmonic oscillators characterized by a Ohmic distributed frequency spectrum.

12

Stochastic Measures and Modular Evolution in Non-Equilibrium Thermodynamics

 

Enrique Hernandez-Lemus, and Jesus K. Estrada-Gil

 

 

 

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We present an application of the theory of stochastic processes to model and categorize non-equilibrium physical phenomena. The concepts of uniformly continuous probability measures and modular evolution lead to a systematic hierarchical structure for (physical) correlation functions and non-equilibrium thermodynamical potentials. It is proposed that macroscopic evolution equations (such as dynamic correlation functions) may be obtained from a non-equilibrium thermodynamical description, by using the fact that extended thermodynamical potentials belong to a certain class of statistical systems whose probability distribution functions are defined by a {\it stationary measure}; although a measure which is, in general, {\sl different} from the equilibrium Gibbs measure. These probability measures obey a certain hierarchy on its stochastic evolution towards the most probable (stationary) measure. This in turns defines a convergence sequence. We propose a formalism which considers the mesoscopic stage (typical of non-local dissipative processes such as the ones described by extended irreversible thermodynamics) as being governed by stochastic dynamics due to the effect of non-equilibrium fluctuations. Some applications of the formalism are described.

13

Beltrami Flow of an Unsteady Dusty Fluid between Parallel Plates in Anholonomic Co-Ordinate System

 

B.J.Gireesha, C.S.Bagewadi and C.S.Vishalakshi

 

 

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An analytical study of Beltrami flow of viscous dusty fluid between two parallel plates has been studied. The flow is due to influence of movement of plates. Flow analysis is carried out using differential geometry techniques and exact solutions of the problem are obtained using Laplace Transform technique also which are discussed with the help of graphs drawn for different values of Reynolds number. Further the expressions for skin-friction are obtained at the boundaries.

14

Exact Solution of The Non - Central Modified Kratzer Potential Plus a Ring - Shaped Like Potential By The Factorization Method

 

J. Sadeghi and B. Pourhassan

 

 

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In this paper, we study the Schr\"odinger equation with a non - central modified Kratzer potential plus a ring – shaped like potential, which is not spherically symmetric. Thus, the standard methods for separation of variables do not quite apply. However we are able to separate variables using a simple extension of the standard method, which leads to solutions in the associated Laguerre function for the radial part and Jacobi polynomials for the polar angle part. We also introduce an interesting pair of first order ladder operators, which allow us to generate the energy eigenvalues for all states of the system. The obtained results show that the lack of spherical symmetry removes the degeneracy of second quantum number m which completely expected.

15

Discrete Self-Similarity between Rr Lyrae Stars And Singly-Excited Helium Atoms

 

Robert L. Oldershaw

 

 

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Classical variable stars called RR Lyrae stars have pulsating outer envelopes constituted of excited atoms. Here we demonstrate that the qualitative and quantitative properties of RR Lyrae variables and one subclass of their atomic scale constituents: singly-excited helium atoms undergoing transitions between Rydberg states, share a remarkable degree of self-similarity. In terms of masses, radii, oscillation periods, morphologies and kinematics the stellar and atomic analogues obey a simple set of discrete self-similar scaling equations. The concept of stellar/atomic self-similarity may prove useful in the search for a deeper understanding of both stellar and atomic systems.

16

Brownian Dynamics of Nanoparticles Moving Near a Fluctuating Membrane

 

A. Bendouch, M. Benhamou, and H. Kaidi

 

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This work deals with Brownian dynamics study of small nanoparticles moving near an attractive penetrable fluid membrane. As consequence, these particles are pushed towards the interface, under a change of a suitable physical parameter, such as temperature, pressure or membrane environment. For simplicity, we assume that the particle size is small enough in comparison to the roughness of the membrane. In addition, the particles are supposed to be of very low density (their mutual interactions can be ignored). Then, the only remaining interaction is a mean-force external potential computed exactly in some recent work. The latter that originates from the strong membrane undulations, is a function of the perpendicular distance $z$. Brownian dynamics are studied through the time particle density, which solves the Smoluchowski equation. This density is determined exactly around the fluid membrane, where the essential of phenomenon takes place. In particular, far from the interface, the beads diffuse as usual. But inside the thermal fluctuations region, the Brownian particles diffuse and effectuate small oscillations, with a frequency \omega scaling as \omega \thicksim \kappa ^{3/8}, where \kappa accounts for the bending rigidity constant of the membrane. We emphasize that the present Brownian dynamics study reveals the existence of a characteristic time \tau \thicksim \kappa ^{-3/4}, which can be interpreted as the time beyond which the particles reach their final equilibrium state. For early times \left( t<\tau \right) , however, the particles are out equilibrium. After a long time \left( t>\tau \right) , the beads reach their final equilibrium state, and occupy new holes and valleys.\ Finally, this work must be considered as a natural extension of a recent one that was concerned with the static study of the colloidal organization in contact with a fluctuating fluid membrane.

17

Influence of Third Order Perturbation on Heisenberg Hamiltonian Of Thick Ferromagnetic Films

 

P. Samarasekara

 

 

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The effect of third order perturbation on the classical Heisenberg Hamiltonian of thick ferromagnetic has been investigated for the first time. Energy of thick films with layers up to 10000 has been plotted for sc(001) and fcc(001) ferromagnetic compounds. Unlike the second order perturbation, the third order perturbation does not increase the total energy by any considerable amount. For the thicknesses approximately N=45 and 40, the anisotropy energy is small for sc(001) and fcc(001), respectively, indicating that the energy required to rotate from easy to hard direction is really small at theses thicknesses. The energy curves of sc (001) and fcc(001) with N=10000 have been flattened by reducing the smooth part of the curve compared with those of second order perturbation. The angle between the easy and hard direction is 97.4^{0} and 32.45^{0 }for sc(001) and fcc(001) thick film with N=10000, respectively. The overshooting parts began to appear after introducing second or third order perturbation, and hence the angle between easy and hard directions is not 90^{0} in the overshooting part of curves. The third and second order perturbation vanish at \theta =0^{0} and 90^{0} directions.

18

Viscous Dusty Fluid Flow with Constant Velocity Magnitude

 

Siddabasappa, Venkateshappa, Rudraswamy, Gopinath

 

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We consider the viscous dusty fluid, where the velocity of the dust particle is everywhere parallel to that of the fluid with velocity magnitude of the fluid is constant along each individual streamline. Also it is assumed that number density of the dust particle is constant and the dust particles are uniform in size and shape and bulk concentration of the dust is small. Hodograph and Legendre transform of stream function is employed to get the solutions and the geometry of streamlines for these flows by using the resulting partial differential equations when the Jacobian is zero and nonzero cases. In each case the variation of pressure is analyzed graphically.

19

The Influence of Long-Range Interaction on Critical Behavior of Some Alloys

 

S. V. Belim

 

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The critical behavior of some alloys are analyzed within the framework of Heisenbergs model with long-range interaction. On based experimental values of the critical exponent \gamma we calculate the value of paerameter of long-range interaction.

 

Volume 5, Issue 18 (June 2008)

 

 

Full text: Acrobat PDF (949 KB)

 

Number 

Articles Title

Abstract

1

Liénard-Wiechert Electromagnetic field

 

R. García-Olivo, R. Linares y M., J. López-Bonilla,  and A. Rangel-Merino

 

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The electromagnetic field generated by a charge in arbitrary motion in Minkowski space is briefly studied. Particularly important is the deduction of the superpotential for the radiative part of  Maxwell tensor.

 

2

On Conformal d'Alembert-Like Equations

 

E. Capelas de Oliveira and R. da Rocha

 

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Using conformal coordinates associated with projective conformal relativity we obtain a conformal Klein-Gordon partial differential equation. As a particular case we present and discuss a conformal `radial' d'Alembert-like equation. As a by-product we show that this `radial' equation can be identified with a one-dimensional Schr\"odinger-like equation in which the potential is exactly the second P\"oschl-Teller potential.

3

Existence of Yang--Mills Theory with Vacuum Vector and Mass Gap

 

Igor Hrncic

 

 

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This paper shows that quantum theory describing particles in finite expanding space--time exhibits natural ultra--violet and infra--red cutoffs as well as posesses a mass gap and a vacuum vector. Having ultra--violet and infra--red cutoffs, all renormalization issues disappear. This shows that Yang--Mills theory exists for any simple compact gauge group and has a mass gap and a vacuum vector.

4

One-parameter potential from Darboux Theorem

 

J García-Ravelo, J J Peña, J Morales, and Shi-Hai Dong

 

 

 

 

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We consider the stationary one-dimensional Schrödinger equation with potential u(x;i)=\sum\limits_{j=-2}^{2}f_{j}(i)x^{j}, where the coefficients f_{j}(i) are functions of a discrete parameter i. We establish the most general form of the coefficients f_{j}(i) and obtain the ladder operators for the solution of Schrödinger equation by a Darboux transform. Generally speaking, the Darboux transform is obtained through a so-called superpotential W(x), which is derived from a Riccati equation. We first propose a convenient \textit{ansatz} for the function % W^{\prime }(x) and then yield a set of nine difference equations for the coefficients f_{j}(i). This set of difference equations establishes the explicit form of the coefficients f_{j}(i), in the potential u(x;i). Our results are consistent with some well-known quantum potentials in special cases.

5

Group Properties of the Black Scholes Equation and its Solutions

 

 

 

J. P. Singh and S. Prabakaran

 

 

 

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Several techniques of fundamental physics like quantum mechanics, field theory and related tools of non-commutative probability, gauge theory, path integral etc. are being applied for pricing of contemporary financial products and for explaining various phenomena of financial markets like stock price patterns, critical crashes etc.. The cardinal contribution of physicists to the world of finance came from Fischer Black {\&} Myron Scholes through the option pricing formula which bears their epitaph and which won them the Nobel Prize for economics in 1997 together with Robert Merton and which constitutes the cornerstone of contemporary valuation theory. They obtained closed form expressions for the pricing of financial derivatives by converting the problem to a heat equation and then solving it for specific boundary conditions. In this paper, we apply the well-entrenched group theoretic methods to obtain various solutions of the Black Scholes equation for the pricing of contingent claims. We also examine the infinitesimal symmetries of the said equation and explore group transformation properties. The structure of the Lie algebra of the Black Scholes equation is also studied.

6

Physical Invariants of Intelligence

 

Michail Zak

 

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The objective of this work is to extend the physical invariants of biosignature (from disorder to order) to invariants of intelligent behavior: {from disorder to order via phase transition}. The approach is based upon the extension of the physics' First Principles that includes behavior of living systems. The new architecture consists of motor dynamics simulating actual behavior of the object, and mental dynamics representing evolution of the corresponding knowledge-base and incorporating it in the form of information flows into the motor dynamics. Due to feedback from mental dynamics, the motor dynamics attains quantum-like properties:its trajectory splits into a family of different trajectories, and each of those trajectories can be chosen with the probability prescribed by the mental dynamics. Intelligence is considered as a tool to preserve and improve survivability of Livings. From the viewpoint of mathematical formalism, it can be associated with the capability to make decisions that {control} the motor dynamics via a feedback from the {mental} dynamics by providing a quantum-like collapse of a random motion into an appropriate deterministic state. Special attention is focused on data-driven discovery of the underlying physical model displaying an intelligent behavior within the proposed formalism.

7

The Numbers Universe: an outline of the Dirac/Eddington numbers as scaling factors for fractal, black hole universes

 

Ross A. McPherson

 

 

 

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The large number coincidences that fascinated theorists such as Eddington and Dirac are shown here to be a specific example of a general set of scaling factors defining universes in which fundamental forces are equated. The numbers have prescriptive power and they are therefore correct and exact {a priori}. The universes thus defined exhibit a fractal structure centred on the Planck/Stoney scale with some formal resemblance to black holes and with properties analogous to Hawking radiation. The problematic case of emerging and evaporating universes is briefly considered in the context of quantum gravity. Historically, the large numbers are associated with the mass of a charged particle and the mass of the universe. This paper demonstrates that the numbers are properly understood in the context of four masses including a non-zero mass derived from Hubble`s Constant and the Planck or Stoney mass.

8

Quantum Analog of the Black- Scholes Formula (market of financial derivatives as a continuous fuzzy measurement

 

S. I. Melnyk, and I. G. Tuluzov

 

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We analyze the properties of optimum portfolios, the price of which is considered a new quantum variable and derive a quantum analog of the Black-Scholes formula for the price of financial variables in assumption that the market dynamics can by considered as its continuous weak measurement at no-arbitrage condition.

9

Faster than Light Quantum Communication

 

A.Y. Shiekh

 

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Faster than light communication might be possible using the collapse of the quantum wave-function without any accompanying paradoxes.

10

Reply to `On a Recent Proposal of Faster than Light Quantum Communication'

 

A.Y. Shiekh

 

Full text: Acrobat PDF (105 KB)

 

 In a recent paper [1] the author proposed the possibility of an experiment to perform faster-than-light communication via the collapse of the quantum wave-function. This was analyzed by Bassi and Ghirardi [2], and it is believed that this analysis itself merits a detailed examination.

 

 

 

Volume 5, Issue 19 (October 2008)

 

Full text: Acrobat PDF 1,685 KB)

 

Number 

Articles Title

Abstract

1

Quantum Computing Through Quaternions

 

J. P. Singh and S. Prabakaran

 

Full text: Acrobat PDF (112 KB)

 

Using quaternions, we study the geometry of the single and two qubit states of quantum computing. Through the Hopf fibrations, we identify geometric manifestations of the separability and entanglement of two qubit quantum systems.

2

Constructible Models of Orthomodular Quantum Logics

 

 

Piotr WILCZEK

 

 

Full text: Acrobat PDF (246 KB)

 

We continue in this article the abstract algebraic treatment of quantum sentential logics [39]. The Notions borrowed from the field of Model Theory and Abstract Algebraic Logic - AAL (i.e., consequence relation, variety, logical matrix, deductive filter, reduced product, ultraproduct, ultrapower, Frege relation, Leibniz congruence, Suszko congruence, Leibniz operator) are applied to quantum logics. We also proved several equivalences between state property systems (Jauch-Piron-Aerts line of investigations) and AAL treatment of quantum logics (corollary 18 and 19). We show that there exist the uniquely defined correspondence between state property system and consequence relation defined on quantum logics. We also signalize that a metalogical property - Lindenbaum property does not hold for the set of quantum logics.

3

Quantum Size Effect of Two Couple Quantum Dots

 

 

Gihan H. Zaki, Adel H. Phillips and Ayman S. Atallah

 

 

Full text: Acrobat PDF (108 KB)

 

The quantum transport characteristics are studied for double quantum dots encountered by quantum point contacts. An expression for the conductance is derived using Landauer - Buttiker formula. A numerical calculation shows the following features: (i) Two resonance peaks appear for the dependence of normalized conductance, G, on the bias voltage, V$_{0}$, for a certain value of the inter barrier thickness between the dots. As this barrier thickness increases the separation between the peaks decreases. (ii) For the dependence of, G, on, Vo, the peak heights decrease as the outer barrier thickness increases. (iii) The conductance, G, decreases as the temperature increases and the calculated activation energy of the electron increases as the dimension, b, increases. Our results were found concordant with those in the literature.

4

Quantum Destructive Interference

 

A.Y. Shiekh

 

Full text: Acrobat PDF (113 KB)

 

An apparent paradox for unitarity non-conservation is investigated for the case of destructive quantum interference.

5

Quantized Fields Around Field Defects

 

Bakonyi G.

 

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A heuristic exercise exploring analogies between different field theories. Similarities between the crystal defects and other various fields help to create a model to quantize these fields. The charge of the electromagnetic field and the electromagnetic waves are used as examples.

6

Path Integral Quantization of Brink-Schwarz Superparticle

 

N. I. Farahat, and H. A. Elegla

 

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The quantization of the Brink-Schwarz superparticle is performed by canonical phase-space path integral.The supersymmetric particle is treated as a constrained system using the Hamilton-Jacobi approach. Since the equations of motion are obtained as total differential equations in many variables, we obtained the canonical phase space coordinates and the phase space Hamiltonian with out introducing Lagrange multipliers and with out any additional gauge fixing condition.

7

Noncommutative Geometry and Modified Gravity

 

N. Mebarki and F. Khelili

 

 

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Using noncommutative deformed canonical commutation relations, a model of gravity is constructed and a schwarchild like static solutions are obtained. As a consequence, the Newtonian potential is modified and it is shown to have a form similar to the one postulated by Fishbach et al. to explain the proposed fifth force. More interesting is the form of the gravitational acceleration expression proposed in the modified Newtonian dynamics theories (MOND) which is obtained explicitly in our model without any ad hoc asymptions.

8

Classification of Electromagnetic Fields in non-Relativist Mechanics

 

 

N. Sukhomlin and M. Arias

 

 

 

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We study the classification of electromagnetic fields using the equivalence relation on the set of all 4-potentials of the Schr\"odinger equation.  In the general case we find the relations among the equivalent fields, currents, and charge densities.  Particularly, we study the fields equivalent to the null field.  We show that the non-stationary state function for a particle in arbitrary uniform time-dependent magnetic field is equivalent to a plane wave.  We present that the known coherent states of a free particle are equivalent to the stationary states of an isotropic oscillator.  We reveal that the only constant magnetic field is not equivalent to the null field (contrary to a constant electrical field) and we find other fields that are equivalent to the constant magnetic field.  We establish that one particular transformation of the free Schr\"odinger equation puts a plane wave and Green's function in a equivalence relation.

9

Magnetized Bianchi Type VI_0 Barotropic Massive String Universe with Decaying Vacuum Energy Density \Lambda.

 

Anirudh Pradhan and Raj Bali

 

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Bianchi type VI_0 massive string cosmological models using the technique given by Letelier (1983) with magnetic field are investigated. To get the deterministic models, we assume that the expansion (\theta) in the model is proportional to the shear (\sigma) and also the fluid obeys the barotropic equation of state. It was found that vacuum energy density \Lambda \propto \frac{1}{t^{2}} which matches with natural units. The behaviour of the models from physical and geometrical aspects in presence and absence of magnetic field is also discussed.

10

Bianchi Type V Magnetized String Dust Universe with Variable Magnetic Permeability

 

Raj Bali

 

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Bianchi Type V magnetized string dust universe with variable magnetic permeability is investigated. The magnetic field is due to an electric current produced along x-axis. Thus F_{23} is the only non-vanishing component of electro-magnetic field tensor F_{ij}. Maxwell's equations F_{[ij;k]} = 0, F_{;j}^{ij} = 0 are satisfied by F_{23} =constant. The physical and geometrical aspects of the model with singularity in the model are discussed. The physical implications of the model are also explained.

11

Dynamics of Shell With a Cosmological Constant

 

A. Eid

 

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Spherically symmetric thin shell in the presence of a cosmological constant are constructed, applying the Darmois-Israel formalism. An equation governing the behavior of the radial pressure across the junction surface is deduced. The cosmological constant term slows down the collapse of matter. The spherical N-shell model with an appropriate initial condition imitates the FRW universe with \Lambda \ne 0, quite well.

12

Discrete Cosmological Self-Similarity and Delta Scuti Variable Stars

 

Robert L. Oldershaw

 

 

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Within the context of a fractal paradigm that emphasizes nature's well-stratified hierarchical organization, the \delta Scuti class of variable stars is investigated for evidence of discrete cosmological self-similarity. Methods that were successfully applied to the RR Lyrae class of variable stars are used to identify Atomic Scale analogues of \delta  Scuti stars and their relevant range of energy levels. The mass, pulsation mode and fundamental oscillation period of a well-studied \delta  Scuti star are then shown to be quantitatively self-similar to the counterpart parameters of a uniquely identified Atomic Scale analogue. Several additional tests confirm the specificity of the discrete fractal relationship.

13

Neutrino Mixings and Magnetic Moments Due to Planck Scale Effects

 

Bipin Singh Koranga

 

 

 

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In this paper, we consider the effect of Planck scale operators on neutrino magnetic moments. We assume that the main part of neutrino masses and mixings arise through GUT scale operators. We further assume that additional discrete symmetries make the neutrino mixing bi-maximal. Quantum gravitational (Planck scale) effects lead to an effective SU(2)_{L}\times U(1) invariant dimension-5 Lagrangian involving neutrino and Higgs fields, which gives rise to additional terms in neutrino mass matrix. These additional terms can be considered to be perturbation of the GUT scale bi-maximal neutrino mass matrix. We assume that the gravitational interaction is flavor blind and we study the neutrino mixings and magnetic moments due to the physics above the GUT scale.

14

Casimir Force in Confined Crosslinked Polymer Blends

 

 

 

 

 

M. Benhamou, A. Agouzouk, H. Kaidi, M. Boughou, S. El Fassi, and A. Derouiche

 

 

 

 

 

 

 

 

 

 

Full text: Acrobat PDF (169 KB)

 

The physical system we consider is a crosslinked polymer blend (or an interpenetrating polymer network), made of two chemically incompatible polymers, which are confined to two parallel plates that are a finite distance L apart, that is L<\xi ^{*}. Here, \xi^{*}\thicksim aD^{-1/2} (a being the monomer size and D the reticulation dose) denotes the size of the microdomains (mesh size). We assume that these strongly adsorb one or the two polymers, near the spinodal temperature (critical adsorption).\ The strong fluctuations of composition give rise to an induced force between the walls we are interested in. To compute this force, as a function of the separation L, we elaborate a field model, of which the free energy is a functional of the composition fluctuation (order parameter). Within the framework of this extended de Gennes theory, we exactly compute this induced force, for two special boundary conditions (symmetric and asymmetric plates). Symmetric plates mean that these have the same preference to adsorb one polymer, while asymmetric ones correspond to the situation where one polymer adsorbs onto the first plate and the other onto the second one. Using the {\em phase portrait} % method, we first show that the induced force is {\em attractive}, for symmetric plates, and {\em repulsive}, for asymmetric ones. Second, we demonstrate that the force satisfies the scaling laws: \Pi _a=\Pi_a^0.\Omega _a\left( L/\xi ^{*}\right)  (symmetric plates) and \Pi _r=\Pi _r^0.\Omega _r\left( L/\xi ^{*}\right)  (asymmetric plates). Here, \Omega_a\left( x\right) and \Omega _r\left( x\right)  are {\em known}universal scaling functions, where \Pi _a^0=-E_aL^{-4} and \Pi_r^0=E_rL^{-4} are the induced forces relative to an uncrosslinked polymer blend confined to the same geometry (E_a and E_r are known amplitudes).\ For very small distances compared to the mesh size \xi ^{*}, we show that, in any case, the force decays exponentially, that is : \Pi _a\simeq -E_aL^{-4}\exp \left\{ -L^2/\xi ^{*\text{ }2}\right\}  and \Pi _r\simeq E_rL^{-4}\exp \left\{ -L^2/\xi ^{*\text{ }2}\right\} . Finally, this work must be regarded as a natural extension of that relative to the uncrosslinked polymer blends.

15

Transport Properties of Thermal Shot Noise Through Superconductor-Ferromagnetic 2DEG Junction

 

 

Attia A. Awad Alla, and Adel H. Phillips

 

 

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We study transport properties of thermal shot noise, thermo power and thermal conductance through superconductor-ferromagnetic /2DEG junction under the effect of Fermi energy, number of open channels and excitation energy. Thermal shot noise, P_{Thermal} is directly related to the conductance through the fluctuation- dissipation theorem; the model consists of a 2DEG region inserted between two identical superconductor electrodes. Ferromagnetic strips are placed onto top of each superconductor/2DEG junction and voltage applied across the model. The results show an oscillatory behavior of the dependence of the thermal shot noise on Fermi energy. These results agree with existing experiments. This research is very important for using a model as a high-frequency shot noise detector.

16

On the Genuine Bound States of a Non-Relativistic Particle in a Linear Finite Range Potential

 

Nagalakshmi A. Rao and B. A. Kagali

 

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We explore the energy spectrum of a non-relativistic particle bound in a linear finite range, attractive potential, envisaged as a quark-confining potential. The intricate transcendental eigenvalue equation is solved numerically to obtain the explicit eigen-energies. The linear potential, which resembles the triangular well, has potential significance in particle physics and exciting applications in electronics.

17

Exact Non-traveling Wave and Coefficient Function Solutions for (2+1)-Dimensional

Dispersive Long Wave Equations

 

 

Sheng Zhang, Wei Wang, and Jing-Lin Tong

 

 

 

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In this paper, a new generalized F-expansion method is proposed to seek exact solutions of nonlinear evolution equations. With the aid of symbolic computation, we choose the (2+1)-dimensional dispersive long wave equations to illustrate the validity and advantages of the proposed method. As a result, many new and more general exact non-traveling wave and coefficient function solutions are obtained including single and combined non-degenerate Jacobi elliptic function solutions, soliton-like solutions and trigonometric function solutions, each of which contains two arbitrary functions. The arbitrary functions provide us with enough freedom to discuss the behaviors of solutions. As an illustrative example, new spatial structures of two solutions are shown. Compared with the most existing F-expansion methods, the new generalized F-expansion method gives not only more general exact solutions but also new formal exact solutions. The proposed method can also be applied to other nonlinear evolution equations in mathematical physics.

                                                                                                           

 

Volume 6, Issue 20 (February 2009)

 

Full text: Acrobat PDF 2,811 KB)

 

Number 

Articles Title

Abstract

1

Macroscopically-Discrete Quantum Cosmology

 

Geoffrey F. Chew

 

Full text: Acrobat PDF (232 KB)

 

Milne's Lorentz-group-based cosmological spacetime and Gelfand-Naimark unitary Lorentz-group representation through transformation of Hilbert-space vectors combine to define a Fock space of `cosmological preons'---quantum-theoretic universe constituents. Lorentz invariance of `age'--\textit{global} \textit{time}-- accompanies Milne's `cosmological principle' that attributes to each spatial location a Lorentz frame. We divide Milne spacetime---the interior of a forward lightcone-- into `slices' of fixed \textit{macroscopic} width in age, with `cosmological rays' defined on (hyperbolic) \textit{slice} \textit{boundaries}. The Fock space of our macroscopically-discrete quantum cosmology (DQC) is defined \textit{only} at these \textit{exceptional} universe ages. Self-adjoint-operator expectations over the ray at any spacetime-slice boundary prescribe throughout the following slice a non-fluctuating continuous `classical reality' represented by Dalembertians, of classical electromagnetic (vector) and gravitational (tensor) potentials, that are current densities of locally-conserved electric charge and energy-momentum. The ray at the upper boundary of a slice is determined from the lower-boundary ray by \textit{branched} slice-traversing \textit{stepped} Feynman paths that carry potential-depending action. Path step is at Planck-scale; branching points represent preon creation-annihilation. Each single-preon wave function depends on the coordinates of a 6-dimensional manifold, one of whose `extra' dimensions associates in Dirac sense to a self-adjoint operator that represents the preon's reversible \textit{local} time. Within a path, local-time \textit{intervals} equal corresponding intervals of monotonically-increasing global time even though, within a (\textit{fixed-age}) ray, the local time of a preon is variable. The operator canonically conjugate to a preon's local time represents its (total) energy in its (Milne) `local frame'. A macroscopically-stable positive-energy single-preon wave function identifies either with a Standard-Model elementary particle or with a graviton. Within intermediate-density sub-Hubble-scale universe regions such as the solar system, where `reproducible measurement' is meaningful, \textit{physical} special relativity---`Poincar\'{e} invariance'---approximates DQC for spacetime scales far above that of Planck.

2

Nonholonomic Ricci Flows: Exact Solutions and Gravity

 

Sergiu I. Vacaru

 

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In a number of physically important cases, the nonholonomically (nonintegrable) constrained Ricci flows can be modelled by exact solutions of Einstein equations with nonhomogeneous (anisotropic) cosmological constants. We develop two geometric methods for constructing such solutions: The first approach applies the formalism of nonholonomic frame deformations when the gravitational evolution and field equations transform into systems of nonlinear partial differential equations which can be integrated in general form. The second approach develops a general scheme when one (two) parameter families of exact solutions are defined by any source—free solutions of Einstein's equations with one (two) Killing vector field(s). A successive iteration procedure results in a class of solutions characterized by an infinite number of parameters for a non--Abelian group involving arbitrary functions on one variable. We also consider nonlinear superpositions of some mentioned classes of solutions in order to construct more general integral varieties of the Ricci flow and Einstein equations depending on infinite number of parameters and three/four coordinates on four/ five dimensional (semi) Riemannian spaces.

3

Killing Symmetries of Deformed Relativity in Five Dimensions

 

Fabio Cardone, Alessio Marrani and Roberto Mignani

 

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This is the first of two papers devoted to investigating the main mathematical aspects of the Kaluza-Klein-like scheme known as Deformed Relativity in five dimensions (DR5). It is based on a five-dimensional Riemannian space in which the four-dimensional space-time metric is deformed (i.e. it depends on the energy) and energy plays the role of the fifth dimension. After a brief survey of the physical and mathematical foundations of DR5, we discuss in detail the Killing symmetries of the theory. In particular, we consider the case of physical relevance in which the metric coefficients are power functions of the energy (Power Ansatz). In order to solve the related Killing equations, we introduce a simplifying hypothesis of functional independence ($\Upsilon $ hypothesis). The explicit expressions of the Killing vectors for the energy-dependent metrics corresponding to the four fundamental interactions (electromagnetic, weak, strong and gravitational) are derived. A preliminary discussion of the infinitesimal-algebraic structure of the Killing symmetries of DR5 is also given.

4

Non commutative Lemaitre-Tolman-Bondi like Metric and Cosmology

 

N.Mebarki, F.Khelili, H.Bouhalouf and O.Mebarki

 

Full text: Acrobat PDF (161 KB)

 

Using noncommutative deformed canonical commutation relations, a model describing gravitation is constructed. A noncommutative Lemaitre- Tolman-Bondi like metric is proposed and non static solutions are discussed. It turns out that in spite of its smallness, the noncommutativity of the geometry plays an important role in unifying the dark matter and energy without any ad hoc assumption, giving a plausible explanation of matter-antimatter asymmetry and controlling the evolution of the universe.

5

Self force on a point-like source coupled with massive scalar field

 

Yurij Yaremko

 

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The problem of determining the radiation reaction force experienced by a scalar charge moving in flat spacetime is investigated. A consistent renormalization procedure is used, which exploits the Poincar\'e invariance of the theory. Radiative parts of Noether quantities carried by massive scalar field are extracted. Energy-momentum and angular momentum balance equations yield Harish-Chandra equation of motion of radiating charge under the influence of an external force. This equation includes effect of particle's own field. The self force produces a time-changing inertial mass.

6

New Jarlskog determiant from Physics above the GUT Scale

 

Bipin Singh Koranga and S. Uma Sankar

 

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We study the Planck scale effects on Jarlskog determiant. Quantum gravitational (Planck scale) effects lead to an effective $SU(2)\times U(1)$ invariant dimension-5 Lagrangian involving neutrino and Higgs fields, which give rise to additional terms in neutrino mass matrix on electroweak symmetry breaking. We assume that gravitational interaction is flavor blind and compute the Jarlskog determiant due to Planck scale effects. In the case of neutrino sector, the strentgh of CP violation is measured by Jarlskog determiant. We applied our approach to study Jarlskog determinant due to the Planck scale effects.

7

Derivation of the Rabbi equation by means of the Pauli Matrices

 

M. De Sanctis and C. Quimbay

 

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The general quantum-mechanical properties of two-level systems  are very relevant for the study of different  physical subjects of great interest, as, for instance, magnetic resonance, nuclear physics, molecular dynamics, masers, neutrino oscillations, quantum computation, etc. In this work we present a nonperturbative approach to the study of the oscillations among two quantum states when an interaction term is considered. First, we show that using a simple parametrization for the superposition of the two states, it is possible to derive easily the Rabbi equation. Next, we show that the Pauli matrices can be conveniently used to write the Hamiltonian operator and to derive the Rabbi equation, directly applying the  time evolution operator to the initial state of the system.

8

Non-interacting spin-1/2 particles in non-commuting external magnetic fields

 

Kunle Adegoke

 

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We obtain, in one dimension, all the energy levels of a system of non-interacting spin-$1/2$ particles in non-commuting external magnetic fields. Examples of how to incorporate interactions as perturbations are given for the Ising model in two orthogonal fields and for the $XZ$ model in two orthogonal fields.

9

An open question: Are topological arguments helpful in setting initial conditions for transport problems and quantization criteria/ quantum computing for Density Wave physics?

 

A.W. Beckwith

 

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The tunneling Hamiltonian is a proven method to treat particle tunneling between different states represented as wavefunctions in many-body physics. Our problem is how to apply a wave functional formulation of tunneling Hamiltonians to a driven sine-Gordon system. We apply a generalization of the tunneling Hamiltonian to charge density wave (CDW) transport problems in which we consider tunneling between states that are wavefunctionals of a scalar quantum field. We present derived I-E curves that match Zenier curves used to fit data experimentally with wavefunctionals congruent with the false vacuum hypothesis. The open question is whether the coefficients picked in both the wavefunctionals and the magnitude of the coefficients of the driven sine Gordon physical system should be picked by topological charge arguments that in principle appear to assign values that have a tie in with the false vacuum hypothesis first presented by Sidney Coleman. Our supposition is that indeed this is useful and that the topological arguments give evidence as to a first order phase transition which gives credence to the observed and calculated I-E curve as evidence of a quantum switching phenomena in density wave physics, one which we think with further development would have applications to quantum computing, via quantum coherent phase evolution, as outlined in this paper.

10

Self-Organization and Emergence in Neural Networks

 

Eliano Pessa

 

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The interest for neural networks stems from the fact that they appear as universal approximators for whatever kind of nonlinear dynamical system of arbitrary complexity. Because nonlinear systems, are studied mainly to model self-organization and emergence phenomena, there is the hope that neural networks can be used to investigate these phenomena in a simpler way, rather than resorting to nonlinear mathematics, with its unsolvable problems. In this contribution we will deal with the conditions granting for the occurring of self-organization and emergence phenomena in neural networks. We will present a number of arguments supporting the claim that emergence is strictly connected to the presence of quantum features in neural networks models.

11

Entanglement Revisited

 

Michail Zak

 

Full text: Acrobat PDF (212 KB)

 

 

Quantum-classical hybrid that preserves the topology of the Schr\"{o}dinger equation (in the Madelung form), but replaces the quantum potential with other, specially selected, function of probability density is introduced. Non-locality associated with a global geometrical constraint that leads to entanglement effect is demonstrated. Despite such a quantum-like characteristic, the hybrid can be of classical scale and all the measurements can be performed classically. This new emergence of entanglement shed light on the concept of non-locality in physics. Application of hybrid systems to instantaneous transmission of conditional information on remote distances is discussed.

12

Innerness of $\rho$--Derivations on Hyperfinite Von Neumann Algebras

 

Madjid Mirzavaziri and Mohammad Sal Moslehian

 

Full text: Acrobat PDF (97 KB)

 

Suppose that $\calm,\caln$ are von Neumann algebras acting on a Hilbert space and $\calm$ is hyperfinite. Let $\rho:{\calm}\to {\caln}$ be an ultraweakly continuous $*$-homomorphism and let $\delta:{\calm}\to{\caln}$ be a $*$-$\rho$-derivation such that $\delta(I)$ commutes with $\rho(I)$. We prove that there is an element $U$ in $\caln$ with $\|U\|\leq\|\delta\|$ such that $\delta(A)=U\rho(A)-\rho(A)U$ for all $A\in{\calm}$.

13

A novel pseudo random bit generator based on chaotic standard map and its testing

 

Vinod Patidar and K. K. Sud

 

Full text: Acrobat PDF (412 KB)

 

 

During last one and half decade an interesting relationship between chaos and cryptography has been developed, according to which many properties of chaotic systems such as: ergodicity, sensitivity to initial conditions/system parameters, mixing property, deterministic dynamics and structural complexity can be considered analogous to the confusion, diffusion with small change in plaintext/secret key, diffusion with a small change within one block of the plaintext, deterministic pseudo randomness and algorithmic complexity properties of traditional cryptosystems. As a result of this close relationship, several chaos based cryptosystems have been put forward since 1990. In one of the stages of the development of chaotic stream ciphers, the application of discrete chaotic dynamical systems in pseudo random bit generation has been widely studied recently. In this communication, we propose a novel pseudo random bit generator (PRBG) based on two chaotic standard maps running side-by-side and starting from random independent initial conditions. The pseudo random bit sequence is generated by comparing the outputs of both the chaotic standard maps. We also present the detailed results of the statistical testing on generated bit sequences, done by using two statistical test suites: the NIST suite and DIEHARD suite, which are developed independently and considered the most stringent statistical test suites to detect the specific characteristics expected of truly random sequences.

14

Heisenberg Hamiltonian with Second Order Perturbation for Spinel Ferrite Ultrathin Films

 

P. Samarasekara, M.K. Abeyratne and S. Dehipawalage

 

Full text: Acrobat PDF (135 KB)

 

The solution of Heisenberg Hamiltonian with second order perturbation will be described for non-oriented spinel cubic ferrimagnetic materials. The perturbation related to the change of angle at the interface of two cells will be considered. The energy peaks become sharper and peak position varies in energy-angle curve as N is increased from 2 to 3. But the separation between two consecutive major maximums remains same. The 3-D plot of total energy versus angle and stress becomes smoother as N is increased from 2 to 3. The energy decreases with number of layers indicating that the behavior of oriented and non-oriented films is different. In N=2 case, minor maximums next to major maximum can be observed. When second order anisotropy constant does not vary within the film with N=2, film behaves as an oriented film.

15

Study of Superconducting State Parameters of Alloy Superconductors

 

Aditya M. Vora

 

Full text: Acrobat PDF (112 KB)

 

The theoretical study of the superconducting state parameters (SSP) viz. electron-phonon coupling strength $\lambda $, Coulomb pseudopotential $\mu ^\ast $, transition temperature $T_C $, isotope effect exponent $\alpha $ and effective interaction strength $N_O V$ of Pb-Tl-Bi alloys viz. Tl$_{0.90}\,$Bi$_{0.10}\,$, Pb$_{0.40}\,$Tl$_{0.60}\,$, Pb$_{0.60}\,$Tl$_{0.40}\,$, Pb$_{0.80}\,$Tl$_{0.20}\,$, Pb$_{0.60}\,$Tl$_{0.20}\,$Bi$_{0.20}\,$, Pb$_{0.90}\,$Bi$_{0.10}\,$, Pb$_{0.80}\,$Bi$_{0.20}\,$, Pb$_{0.70}\,$Bi$_{0.30}\,$, Pb$_{0.65}\,$Bi$_{0.35}\,$ and Pb$_{0.45\,}$Bi$_{0.55}\,$ have been made extensively in the present work using a model potential formalism for the first time. A considerable influence of various exchange and correlation functions on $\lambda $ and $\mu ^\ast $ is found from the present study. The present results of the SSP are found in qualitative agreement with the available experimental data wherever exist.

16

Riemann Zeta Function Zeros Spectrum

 

Igor Hrncic

 

 

Full text: Acrobat PDF (169 KB)

 

This paper shows that quantum chaotic oscillator Hamiltonian $H=px$ generates Riemann zeta function zeros as energy eigenvalues assuming validity of the Riemann hypothesis. We further put this on a firmer ground proving rigorously the Riemann hypothesis. We next introduce reformulation of special theory of relativity by which chaotic oscillator motion described via Hamiltonian $H=px$ is generated by gravitational potential, thus linking chaotic motion and Riemann zeta function to gravity.

17

Gaussian Delay Models for Light Broadenings and Redshifts

 

B. Lacaze

 

Full text: Acrobat PDF (151 KB)

 

In astronomy light emission is characterized by a frequency $\omega {0}/2\pi $, a redshift $z$ (sometimes a blueshift), a FWHM (Full Width Half Maximum) and an EW (Equivalent Width). $\omega _{0}$ relates to the nature of the concerned atom or molecule, $z$ allows to determine the speed and the distance of the body through the Hubble law, FWHM measures the wave spectral width, and EW defines a kind of SNR (Signal-to-Noise Ratio). In this paper, we show that Gaussian time delays on pure waves can theoretically explain the width of emission lines, any redshift and a floor noise which can be matched to any EW.

18

Eigenfunctions of Spinless Particles in a One-dimensional Linear Potential Well

 

Nagalakshmi A. Rao and B. A. Kagali

 

Full text: Acrobat PDF (91 KB)

 

 

In the present paper, we work out the eigenfunctions  of spinless particles bound in a one-dimensional linear finite  range, attractive potential well, treating it as a time-like component of a four-vector. We show that the one-dimensional stationary Klein-Gordon equation is reduced to a standard differential equation, whose solutions, consistent with the boundary conditions, are the parabolic cylinder functions, which further reduce to the well-known confluent hypergeometric functions.

                                                                                                           

 

 

Volume 6, Issue 21 (May 2009)

 

Full text: Acrobat PDF 1,502 KB)

 

Number 

Articles Title

Abstract

1

Editorial

 

Ammar Sakaji

 

Full text: Acrobat PDF (40 KB)

 

 

2

The Tolman-Regge Antitelephone Paradox: Its Solution by Tachyon Mechanics

 

E. RECAMI

 

Full text: Acrobat PDF (112 KB)

 

The possibility of solving (at least \in microphysics") all the ordinary causal paradoxes devised for tachyons is not yet widely recognized; on the contrary, the effectiveness of the Stuckelberg-Feynman switching principle is often misunderstood. We want, therefore, to show in detail and rigorously how to solve the oldest causal paradox, originally proposed by Tolman, which is the kernel of so many further tachyon paradoxes. The key to the solution is a careful application of tachyon kinematics, which can be unambiguously derived from special relativity. A systematic, thorough analysis of all tachyon paradoxes is going to appear elsewhere..

EJTP is reproducing E. Recami's original paper: Lett. Nuovo Cimento, 44, 587 (1985).

3

New Physical Principle for Monte-Carlo simulations

 

Michail Zak

 

Full text: Acrobat PDF (104 KB)

 

New physical principle for Monte-Carlo simulations has been introduced. It is based upon coupling of dynamical equations and the corresponding Liouville equation. The proposed approach does not require a random number generator since randomness is generated by instability of dynamics triggered and controlled by the feedback from the Liouville equation. Direct simulation of evolutionary partial differential equations have been proposed, discussed, and illustrated.

4

First Passage Random Walk of Coupled Detector-System Pairs and Quantum Measurement

 

Fariel Shafee

 

Full text: Acrobat PDF (140 KB)

 

We propose a new model for a measurement of a characteristic of a microscopic quantum state by a large system that selects stochastically the different eigenstates with appropriate quantum weights. Unlike previous works which formulate a modified Schrödinger equation or an explicit modified Hamiltonian, or more complicated mechanisms for reduction and decoherence to introduce transition to classical stochasticity, we propose the novel use of couplings to the environment, and random walks in the product Hilbert space of the combined system, with first passage stopping rules, which seem intuitively simple, as quantum weights and related stochasticity is a commonality that must be preserved under the widest range of applications, independent of the measured quantity and the specific properties of the measuring device.

5

Underdeterminacy and Redundance in Maxwell's Equations. I. The Origin of Gauge Freedom

 

Peter Enders

 

Full text: Acrobat PDF (132 KB)

 

The gauge freedom in the electromagnetic potentials indicates an underdeterminacy in Maxwell's theory. This underdeterminacy will be found in Maxwell's (1864) original set of equations by means of Helmholtz's (1858) decomposition theorem. Since it concerns only the longitudinal electric field, it is intimately related to charge conservation, on the one hand, and to the transversality of free electromagnetic waves, on the other hand (as will be discussed in Pt. II). Exploiting the concept of Newtonian and Laplacian vector fields, the role of the static longitudinal component of the vector potential being not determined by Maxwell's equations, but important in quantum mechanics (Aharonov-Bohm effect) is elucidated. These results will be exploited in Pt.III for formulating a manifest gauge invariant canonical formulation of Maxwell's theory as input for developing Dirac's (1949) approach to special-relativistic dynamics.

 

6

The Origin of Mass, Spin and Interaction

 

B.G. Sidharth

 

Full text: Acrobat PDF (103 KB)

We argue that a non commutative geometry at the Compton scale is at the root of mass, Quantum Mechanical spin and QCD and electromagnetic interactions. It also leads to a reconciliation of linearized General Relativity and Quantum Theory.

7

Nonholonomic Ricci Flows and Parametric Deformations of the Solitonic pp{Waves and Schwarzschild Solutions

 

Sergiu I. Vacaru

 

Full text: Acrobat PDF (231 KB)

 

We study Ricci flows of some classes of physically valuable solutions in Einstein and string gravity. The anholonomic frame method is applied for generic off-diagonal metric ansatz when the field/ evolution equations are transformed into exactly integrable systems of partial differential equations. The integral varieties of such solutions, in four and five dimensional gravity, depend on arbitrary generation and integration functions of one, two and/ or three variables. Certain classes of nonholonomic frame constraints allow us to select vacuum and/or Einstein metrics, to generalize such solutions for nontrivial string (for instance, with antisymmetric torsion fields) and matter field sources. A very important property of this approach (originating from Finsler and Lagrange geometry but re-defined for semi-Riemannian spaces) is that new classes of exact solutions can be generated by nonholonomic deformations depending on parameters associated to some generalized Geroch transforms and Ricci flow evolution. In this paper, we apply the method to construct in explicit form some classes of exact solutions for multi{parameter Einstein spaces and their nonholonomic Ricci flows describing evolutions/interactions of solitonic pp{waves and deformations of the Schwarzschild metric. We explore possible physical consequences and speculate on their importance in modern gravity.

8

Relativistic Effects on Quantum Bell States of Massive Spin 1/2 Particles

 

J. P. Singh

 

Full text: Acrobat PDF (195 KB)

 

We examine the behaviour of the maximally entangled Bell state of two spin 1/2 massive particles under relativistic transformations. On the basis of explicit calculations of the Wigner rotation and the use of transformation properties of Dirac spinors, we establish that the constituent particles of the Bell state undergo momentum dependent rotation of the spin orientations characterized by the Wigner angle \phi _{W} =\tan ^{-1} \frac{\sinh \varpi \sinh \tau }{\cosh \varpi +\cosh \tau }. However, since local unitarity is retained in the process, the corresponding entanglement fidelity is not lost.

9

Partial Swapping, Unitarity and No-signalling

 

I. Chakrabarty, and B. S. Choudhury 

 

Full text: Acrobat PDF (83 KB)

 

It is a well known fact that a quantum state |\psi(\theta,\phi)\rangle is represented by a point on the Bloch sphere, characterized by two parameters \theta  and \phi. In a recent work we already proved that it is impossible to partially swap these quantum parameters. Here in this work we will show that this impossibility theorem is consistent with principles like unitarity of quantum mechanics and no signalling principle.

10

Time scale synchronization between two different time-delayed systems

 

Dibakar Ghosh

 

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In this paper we consider time scale synchronization between two different time-delay systems. Due to existence of intrinsic multiple characteristic time scales in the chaotic time series, the usual definition for the calculation of phase failed. To define the phase, we have used empirical mode decomposition and the results are compared with those from continuous wavelet transform. We investigate the generalized synchronization between these two different chaotic time delay systems and find the existence condition for the generalized synchronization. It has been observed that the generalized synchronization is a weaker than the phase synchronization. Due to the presence of scaling factor in the wavelet transform it has more flexibility for application.

11

Thermodynamic Fluctuation Theory and Gravitational Clustering of Galaxies

 

Mohd Shafi Khan, Naseer Iqbal and Farooq Ahmad

 

Full text: Acrobat PDF (100 KB)

 

 

We study the phase transitions occurring in the gravitational clustering of galaxies on the basis of thermodynamic fluctuation theory. This is because the fluctuations in number and energy of the particles are constantly probing the possibility of a phase transition. A calculation of various moments of the fluctuating thermodynamic extensive parameters like the number and energy fluctuations, has been performed. The correlated fluctuations \left< \bigtriangleup N \bigtriangleup U \right>, have shown some interesting results. For weak correlations, their ensemble average is positive, indicating that a region of density enhancement typically coincides with a region of positive total energy. Its perturbed kinetic energy exceeds its perturbed potential energy. Similarly an underdense region has negative total energy since it has preferentially lost the kinetic energy of the particles that have fled. For larger correlations the overdense regions typically have negative total energy, underdense regions have positive total energy. The critical value at which this switch occurs is the critical temperature T= T_C, whose value has been calculated analytically. At this critical value T_C, a positive \left<\bigtriangleup N\right> is just as likely to be associated with a positive or a negative \bigtriangleup U.

12

Neutrino Oscillation Probability from Tri-Bimaximality due to Planck Scale Effects

 

Bipin Singh Koranga

 

Full text: Acrobat PDF (102 KB)

 

Current neutrino experimental data on neutrino mixing are well describes by Tri-bi-maximal mixing, which is predicts sin^{2}\theta_{12}=1/3,; zero U_{e3} and \theta_{23}=45^{o}. We consider the Planck scale operator on neutrino mixing. We assume that the neutrino masses and mixing arise through physics at a scale intermediate between Planck scale and the electroweak braking scale. We also assume, that just above the electroweak breaking scale neutrino mass are nearly degenerate and the mixing is tri-bi-maximal. Quantum gravity (Planck scale) effects lead to an effective SU(2)_{L}\times U(1) invariant dimension-5 Lagrangian symmetry involving Standard Model. On electroweak symmetry breaking, this operator gives rise to correction to the neutrino masses and mixings these additional terms can be considered as perturbation to the tri-bimaximal neutrino mass matrix. We compute the deviation of the three mixing angles and oscillation probability. We find that the only large change in solar mixing angle and  change in maximum P_{\mu e} is about 10%.

13

Representation of su(1,1) Algebra and Hall Effect

 

J. Sadeghi and B. Pourhassan

 

Full text: Acrobat PDF (88 KB)

 

 

In this paper we consider the Schwinger and Heisenberg representation of su(1,1) algebra under Hall effect. In presence of magnetic field, we obtain the generators of su(1,1) algebra in terms of ladder operators, and magnetic field for the one and two bosons system. Also the Casimir operator for both systems are obtained by ladder operators.

14

Some LRS Bianchi Type VI0 Cosmological Models with Special Free Gravitational Fields

 

Raj Bali, Ratna Banerjee, and S.K.Banerjee

 

Full text: Acrobat PDF (104 KB)

 

The properties of the free gravitational fields and their invariant characterizations are discussed and also obtained LRS Bianchi type VI0 cosmological models imposing different conditions over the free gravitational fields. Models thus formed are then discussed in detail with respect to their physical and kinematical parameters in the last section of the paper.

15

The Motion of A Test Particle in the Gravitational Field of A Collapsing Shell

 

A. Eid, and A. M. Hamzay

 

Full text: Acrobat PDF (115 KB)

 

We use the Israel formalism to describe the motion of a test particle in the gravitational field of a collapsing shell. The formalism is developed in both of Schwarzchild and Kruskal coordinates.

 

           

Volume 6, Issue 22 (October 2009)

 

Full text: Acrobat PDF 3,190 KB)

 

Number 

Articles Title

Abstract

1

Foreword

 

Ignazio Licata

 

Full text: Acrobat PDF (30 KB)

 

 

2

Equivalence Principle and Field Quantization in Curved Spacetime

 

H. Kleinert

 

Full text: Acrobat PDF (93 KB)

 

To comply with the equivalence principle, fields in curved spacetime can be quantized only in the neighborhood of each point, where one can construct a freely falling Minkowski frame with zero curvature. In each such frame, the geometric forces of gravity can be replaced by a selfinteracting spin-2 field, as proposed by Feynman in 1962. At a fixed distance $R$ from a black hole, the vacuum in each freely falling volume element acts like a thermal bath of all particles with Unruh temperature T_U=\hbar GM/2\pi c R^2. At the horizon R=2GM/c^2, the falling vacua show the Hawking temperature T_H=\hbar c^3/8\pi GMk_B

 

3

New Seiberg-Witten Fields Maps Through Weyl Symmetrization and the Pure Geometric Extension of The Standard Model

 

N. Mebarki; F. Khelili and O. Benabbes

 

Full text: Acrobat PDF (183 KB)

 

A unified description of a symmetrized and anti-symmetrized Moyal star product of the noncommutative infinitesimal gauge transformations is presented and the corresponding Seiberg-Witten maps are derived. Moreover, the noncommutative covariant derivative, field strength tensor as well as gauge transformations are shown to be consistently constructed not on the enveloping but on the Lie and/or Poisson algebra. As an application, a pure geometric extension of the standard model is shown explicitly.

4

A Method for Constructing a Lax Pair for the Ernst Equation

 

C. J. Papachristou  and B. Kent Harrison

 

Full text: Acrobat PDF (118 KB)

 

A systematic construction of a Lax pair and an infinite set of conservation laws for the Ernst equation is described. The matrix form of this equation is rewritten as a differential ideal of (2,R)-valued differential forms, and its symmetry condition is expressed as an exterior equation which is linear in the symmetry characteristic and has the form of a conservation law. By means of a recursive process, an infinite collection of such laws is then obtained, and the conserved ``charges'' are used to derive a linear exterior equation whose components constitute a Lax pair.

5

Plane Symmetric Viscous Fluid Universe in Lyra Geometry

 

Pratima Singh  and Pawan Kumar Rai

 

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A new class of plane-symmetric homogeneous cosmological models for viscous fluid distribution is obtained in the context of Lyra's geometry. We have obtained two types of solutions by considering the uniform as well as time dependent displacement field. To get the deterministic solutions of Einstein's modified field equations, the free gravitational field is assumed to be of type D which is of the next order in the hierarchy of Petrov classification. It has been found that the displacement vector $\beta$ behaves like cosmological term \Lambda in the normal gauge treatment and the solutions are consistent with the observations. The displacement vector \beta(t) affects entropy. Some physical and geometric properties of the models are discussed.

 

6

Some Bianchi Type I Cosmological Models of the Universe for Viscous Fluid Distribution in Lyra Geometry

 

Ravi Prakash Singh and Lallan Yadav

 

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Some Bianchi type I cosmological models of the universe with time dependent gauge function $\beta$ for viscous fluid distribution within the framework of Lyra geometry are investigated in which the expansion is considered only in two dimensions i.e. one of the Hubble parameter (H_{1} = \frac{\dot{A}}{A}) is zero. To get the deterministic solutions of Einstein's modified field equations, the viscosity coefficient of bulk viscous fluid is assumed to be a power function of mass density and the coefficient of shear viscosity is considered as constant in first case whereas in other case it is taken as proportional to scale of expansion in the model. It has been found that the displacement vector \beta(t) behaves like cosmological term \Lambda in the normal gauge treatment and the solutions are consistent with the observations. Solution in absence of shear viscosity is also obtained. The displacement vector \beta(t) affects entropy. Some physical and geometrical properties of the models are discussed.

7

Geometrical Behaviuors of LRS Bianchi Type-I Cosmological Model

 

Hassan Amirhashchi, Hishamuddin Zainuddin and Hamid Nil Saz Dezfouli

 

Full text: Acrobat PDF (84 KB)

 

By using Einstein's theory of general relativity some properties of spatially homogeneous locally rotationally symmetric (LRS) Bianchi type-I space-time are investigated in empty space. The concept of Riemannian curvature tensor, Ricci tensor and Ricci scalar has been used to discuss the geometrical behavior of the space-time. It is shown that, LRS Bianchi type-I has always flat geometry in empty space. Also we have shown that the vacuum model does not have singularity when time goes to zero.

8

Bianchi Type V Bulk Viscous Cosmological Models with Time Dependent Lambda Λ Term

 

J. P. Singh and P. S. Baghel

 

Full text: Acrobat PDF (119 KB)

 

Spatially homogeneous and anisotropic Bianchi type V space-time with bulk viscous fluid source and time-dependent cosmological term are considered. Cosmological models have been obtained by assuming a variation law for the Hubble parameter which yields a constant value of deceleration parameter. Physical and kinematical parameters of the models are discussed. The models are found to be compatible with the results of cosmological observations.

9

Corrections to massive neutrino masses, caused by vacuum polarisation in strong Coulomb field of daughter nuclei in weak decays of heavy ions

 

N. Ivanov, P. Kienle, E. L. Kryshen,  and M. Pitschmann

 

Full text: Acrobat PDF (159 KB)

 

We calculate corrections to masses of massive neutrino   mass--eigenstates, caused by vacuum polarization in the strong  Coulomb fields of daughter heavy nuclei in the K--shell electron  capture decays (EC) and positron (\beta^+) decays of highly  ionized heavy ions, investigated experimentally at GSI in  Darmstadt. Some applications of the obtained results are discussed.

10

Neutrino Mass Differences and Nonunitarity of Neutrino Mixing Matrix from Interfering Recoil Ions

 

H. Kleinert  and P. Kienle

 

Full text: Acrobat PDF (222 KB)

 

We show that the recent observation of the time modulation of two-body weak decays of heavy ions reveals the  mass content  of the electron neutrinos via interference patterns in the recoiling ion wave function. From the modulation period we derive the difference of the square masses \Delta m^2\approx 22.5\times 10^{-5}$\,eV${}^2, which is about 2.8 times larger than that derived from a combined analysis of KamLAND and solar neutrino oscillation experiments. It is, however, compatible with a data regime to which the KamLAND analysis attributes a smaller probability. The experimental results displayed in Fig.~1 imply that the neutrino mixing matrix violates unitarity by about 10\%.

11

Bifurcations of fractional-order diffusionless Lorenz system

 

Kehui Sun and J. C. Sprott

 

Full text: Acrobat PDF (1,886 KB)

 

 

Using the predictor-corrector scheme, the fractional-order diffusionless Lorenz system is investigated numerically. The effective chaotic range of the fractional-order diffusionless system for variation of the single control parameter is determined. The route to chaos is by period-doubling bifurcation in this fractional-order system, and some typical bifurcations are observed, such as the flip bifurcation, the tangent bifurcation, an interior crisis bifurcation, and transient chaos. The results show that the fractional-order diffusionless Lorenz system has complex dynamics with interesting characteristics.

12

Underdeterminacy and redundance in Maxwell’s Equations

 

Peter Enders

 

Full text: Acrobat PDF (225 KB)

 

Maxwell's (1864) original equations are redundant in their description of charge conservation. In the nowadays used, 'rationalized' Maxwell equations, this redundancy is removed through omitting the continuity equation. Alternatively, one can Helmholtz decompose the original set and omit instead the longitudinal part of the flux law. This provides at once a natural description of the transversality of free electromagnetic waves and paves the way to eliminate the gauge freedom. Poynting's inclusion of the longitudinal field components in his theorem represents an additional assumption to the Maxwell equations. Further, exploiting the concept of Newtonian and Laplacian vector fields, the role of the static longitudinal component of the vector potential being \emph{not} determined by Maxwell's equations, but important in quantum mechanics (Aharonov-Bohm effect) is elucidated. Finally, extending Messiah's (1999) description of a gauge invariant canonical momentum, a manifest gauge invariant canonical formulation of Maxwell's theory \emph{without} imposing any contraints or auxiliary conditions will be proposed as input for Dirac's (1949) approach to special-relativistic dynamics.

13

The Proton as A Kerr-Newman Black Hole

 

Robert L. Oldershaw

 

Full text: Acrobat PDF (72 KB)

 

 

The general equation governing the mass, spin and angular momentum of a Kerr-Newman black hole applies equally well to a proton when the gravitational coupling constant predicted by a discrete fractal paradigm is used in the equation, along with the standard mass, spin and angular momentum of the proton.

14

Self-Interacting Scalar Field and Galactic Dark Halos

 

M. R. Bordbar and N. Riazi

 

Full text: Acrobat PDF (217 KB)

 

We construct dark halo models which are supported by a self-interacting scalar field. The possibility that the energy density of such a field which could produce dark matter and dark energy inside and outside of the galactic dark halos is explored.

15

Path Integral Quantization of The Electromagnetic Field Coupled to A Spinor

 

Walaa. I. Eshraim and Nasser. I. Farahat

 

Full text: Acrobat PDF (94 KB)

 

The Hamilton-Jacobi approach is applied to the electromagnetic field coupled to a spinor. The integrability conditions are investigated and the path integral quantization is performed using the action given by Hamilton-Jacobi approach.

16

Neutrino Mixing and Cosmological Constant above GUT Scale

 

Bipin Singh Koranga

 

Full text: Acrobat PDF (99 KB)

 

Neutrino mixing lead to a non zero contribution to the cosmological constant. We consider non renormalization $1/M_{x}$ interaction term as a perturbation of the neutrino mass matrix. We find that for the degenerate neutrino mass spectrum. We assume that the neutrino masses and mixing arise through physics at a scale intermediate between Planck Scale and the electroweak scale. We also assume, above the electroweak breaking scale, neutrino masses are nearly degenerate and their mixing is bimaximal. Quantum gravitational (Planck scale) effects lead to an effective $SU(2)_{L}\times U(10$ invariant dimension-5 Lagrangian involving neutrino and Higgs fields, which gives rise to additional terms in neutrino mass matrix. There additional term can be considered to be perturbation of the GUT scale bi-maximal neutrino mass matrix. We assume that the gravitational interaction is flavour blind and we study the neutrino mixing and cosmological constant due to physics above the GUT scale.

 

17

The Restricted Three Body Problem with Quadratic Drag

 

Mayer Humi

 

Full text: Acrobat PDF (207 KB)

 

When an asteroid, space-craft or another small object in the solar system is in the vicinity of a planet it is subjected to the gravitational forces of the Sun, the planet, the drag forces due to the solar wind and (possibly) the planet upper atmosphere. To determine the object trajectory we consider this problem within the context of the restricted three body problem in three dimensions with quadratic drag. In this setting we linearize the equations of motion of the object and cast them in a coordinate system with respect to the secondary (planet) which is assumed to be in a general Keplerian orbit around the primary (Sun). We then reduce them, to a simple system of three second order linear differential equations. These equations can be considered to be a generalization of Hill's equations to general Keplerian orbits (of the secondary) with the addition of quadratic drag force acting on the third object in the system. We derive also "approximate conservation laws" in three dimensions which represent a generalization of Jacobi's integral in two dimensions and consider some special cases.

 

                                                                                                           

 

Volume 7, Issue 23 (March 2010)

 

Full text: Acrobat PDF 4,026 KB)

 

Number 

Articles Title

Abstract

1

Preface

 

Ignazio Licata

 

Full text: Acrobat PDF (29 KB)

 

 

2

Symmetry, Conserved Charges, and Lax Representations of Nonlinear Field Equations: A Unified Approach

 

C. J. Papachristou

Full text: Acrobat PDF (129 KB)

 

A certain non-Noetherian connection between symmetry and integrability properties of nonlinear field equations in conservation-law form is studied. It is shown that the symmetry condition alone may lead, in a rather straightforward way, to the construction of a Lax pair, a doubly infinite set of (generally nonlocal) conservation laws, and a recursion operator for symmetries. Applications include the chiral field equation and the self-dual Yang-Mills equation.

3

Electroweak Standard Model at Finite Temperature in Presence of A Bosonic Chemical Potential

 

Pena and C. Quimbay

 

Full text: Acrobat PDF (168 KB)

 

We study the electroweak standard model at finite temperature in presence of a bosonic chemical potential associated with the conserved electromagnetic current. To preserve the thermodynamic equilibrium of the system, the thermal medium is neutralized by the introduction of four background charges related to the four gauge bosons of this model. Using the mean-field approximation, in the high temperature limit, we find that there exists a difference between the effective mass of the spatial and temporal components of the W boson. A W boson condensation induced via the background charges allows to vanish this difference.

4

Electric Dipole Moment and Neutrino Mixing due to Planck Scale Effects

 

Bipin Singh Koranga

 

Full text: Acrobat PDF (97 KB)

 

In this paper, we consider the effect of Planck scale operators on electric dipole moment of the electron $de$. The electric dipole moment of the electron, $de$ is known to vanish up to three loops in the standard model with massless neutrinos We consider the Planck scale operator on neutrino mixing. We assume that the neutrino masses and mixing arise through physics at a scale intermediate between Planck scale and the electroweak breaking scale. We also assume, that just above the electroweak breaking scale neutrino mass are nearly degenerate and the mixing is bi-maximal. Quantum gravity (Planck scale) effects lead to an effective SU(2)_{L} U(1) invariant dimension-5 Lagrangian symmetry involving Standard Model. On electroweak symmetry breaking, this operator gives rise to correction to the neutrino masses and mixings these additional terms can be considered as perturbation to the bimaximal neutrino mass matrix We assume that the gravitational interaction is flavour blind and we study the neutrino mixing and electric dipole moment due to the Planck scale effects.

5

Spinless Relativistic Particle in the Presence of A Minimal Length

 

M. Merad, F. Zeroual, and H. Benzair

Full text: Acrobat PDF (151 KB)

 

In this paper, we propose to study the (1+1)-dimensional Klein-Gordon equation in the presence of a minimal length by two approaches: a method direct in the position space representation and a path integral formalism in energy-momentum space, where a particle is subjected to a mixing of \ linear vector plus scalar potentials. For a first method, a suitable approximation technique of a non-relativistic quantum mechanics has been applied and the shifts of the relativistic energy levels is determined. For a second method, the Green function is obtained, the energy spectrum together with the normalized wave functions of the bound states are deduced \ and the limiting case is considered. The results of both methods are compared and we find the same dominant quantities to order 1 on parameter of deformation.

6

Astrophysical Chaotic Gun Effect

 

Gheorghe Dumitrescu

 

Full text: Acrobat PDF (185 KB)

We propose a kinetic equation for a special kind of acceleration: chaotic gun effect. Then we infer a distribution function which can depict the instability condition. With this distribution function we derive the power spectrum of the synchrotron emission and we prove the power law form of the power spectrum. We show that the spectral index of the emission spectrum is related to the spectral index of the number of the charged particles in the beam. Our numeric simulations show that the spectrum has a break at a frequency threshold where the chaotic acceleration becomes efficient. Assuming this threshold to the set on of the efficient chaotic gun effect we estimate the magnetic strength .Our paper advocates an electromagnetic process able to accelerate charged particles to high energies starting from low energies. Assuming the high-energy particles spectra of Mkn 501 to be produced by the synchrotron emission during chaotic gun effect we estimate some parameters of the source.

7

Chaos in Quantum Chromodynamics and the Hadron Spectrum

 

Ervin Goldfain

 

Full text: Acrobat PDF (114 KB)

 

We present analytic evidence that the distribution of hadron masses follows from the universal transition to chaos in non-equilibrium field theory. It is shown that meson and baryon spectra obey a scaling hierarchy with critical exponents ordered in natural progression. Numerical predictions are found to be in close agreement with experimental data.

8

Towards The Determination of Properties of the Unconventional Josephson Junction Made by Putting Non-Superconducting Strip on the Top of Superconducting Strip

 

Krzysztof Pomorski and Przemyslaw Prokopow

 

Full text: Acrobat PDF (1,652 KB)

 

We present the theoretical approach to study the unconventional Josephson junction (uJJ) made by putting the non-superconducting strip on the top of superconducting strip. We work in the framework of the Ginzburg-Landau, Bogoliubov de Gennes and Usadel equations. Then we solve the non-linear partial differential equations numerically for few simple cases. We review the similarities and new aspects of uJJ with currently known Josephson junctions. Basing on the obtained results and current knowledge on Josephson junctions we point the future perspectives of the research on uJJs.

9

An Interruption in the Highway: New Approach to Modeling the Car-Traffic

 

Amin Rezaeezadeh

 

Full text: Acrobat PDF (285 KB)

 

A very common phenomena in car-traffic system is investigated in this article. The problem is one-dimensional. We try to find the wave equation of the traffic and then, we'll talk more about the simulation of the system using Matlab7.6.

10

A generalization of the Three-Dimensional Harmonic Oscillator Basis for Wave Functions with Non-Gaussian Asymptotic Behavior

 

Maurizio De Sanctis

 

Full text: Acrobat PDF (102 KB)

 

Starting from the standard harmonic oscillator basis, we construct new sets of orthonormal wave functions  with non-Gaussian asymptotic spatial dependence. These new wave functions can be used to study at numerical level two-body bound systems like mesons and baryons within quark-diquark models. Generalized hyperradial functions for three-quark models are also studied.

11

Exactly solved potentials generated from the Manning-Rosen potential using extended transformation method

 

S. A. S. Ahmed and  L. Buragohain

 

Full text: Acrobat PDF (113 KB)

 

 

Generation of exactly solvable quantum systems in non-relativistic quantum mechanics from an already analytically solved quantum system is presented using extended transformation method. The bound state quantized energy spectra and the corresponding wavefunctions of the generated potentials are obtained. It is also shown that eigenfunctions of the new quantum systems can easily be normalized.

12

On the Bound-State Spectrum of A Nonrelativistic Particle in the Background of A Short-Ranged Linear Potential

 

L.B. Castro and A.S. de Castro

 

Full text: Acrobat PDF (118 KB)

 

 

The nonrelativistic problem of a particle immersed in a triangular potential well, set forth by N. A. Rao and B. A. Kagali, is revised. It is shown that these researchers misunderstood the full meaning of the potential and obtained a wrong quantization condition. By exploring the space inversion symmetry, this work presents the correct solution to this problem with potential applications in electronics in a simple and transparent way.

13

Relativistic Spin Operator with Observers in Motion

 

J. P. Singh

 

Full text: Acrobat PDF (156 KB)

 

 

We obtain transformation equations for the Bell basis states under an arbitrary Lorentz boost and compute the expectation values of the relativistic center of mass spin operator under each of these boosted states. We also obtain expectation values for spin projections along the axes.

14

Statistical Mechanics of Classical N-Particle System of  Galaxies in the Expanding Universe

 

Farooq Ahmad and Abdul Wahid

 

Full text: Acrobat PDF (101 KB)

 

For the distribution of classical non-interacting particles we use Maxwell-Boltzmann's statistics. However, this statistics is not workable for classical interacting particles (galaxies). We attempt to modify the Maxwell-Boltzmann's statistics by incorporating gravitational interaction term in it. The number of ways in which N-particles can have pair interaction due to gravitational interaction is obtained. With the help of entropy maximization we derive the analytical expression for occupation number. Using the modified statistics we obtain the general expressions for different thermodynamical quantities and attempt to derive general distribution function for gravitating particles (galaxies).

15

On the Noncommutative Space-time Bianchi I Universe and Particles Pair Creation Process

 

N. Mebarki, L. Khodja and S. Zaim

 

Full text: Acrobat PDF (155 KB)

 

Using an approach of modified Euler-Lagrange field equations obtained from an invariant action under infinitesimal modified general coordinates, local Lorentz and U_{\ast }(1) gauge transformations together with the corresponding Seiberg-Witten maps of the dynamical fields, a generalized Dirac equation in the presence of a constant electric field and a noncommutative cosmological anisotropic Bianchi I universe is derived and the particles pair creation process is studied.

16

Cylindrically Symmetric Inhomogeneous String Cosmological Models of Perfect Fluid Distribution with Electromagnetic Fields

 

Anirudh Pradhan and Rekha Singh

 

Full text: Acrobat PDF (139 KB)

 

Two new cylindrically symmetric inhomogeneous string cosmological models are investigated in presence of magnetic field. We have assumed that F_{12} is the only non-vanishing component of electromagnetic field tensor F_{ij}. The Maxwell's equations show that F_{12} is the function of $x$ alone whereas the magnetic permeability \bar{\mu} is the function of x and t both. To get the deterministic solution, it has been assumed that the metric coefficients are separable in the form as A = f(x) \ell(t), B = g(x) k(t), C = g(x) \nu(t). Also, the Einstein field equations have been solved with string source in which magnetic field is absent. Some physical and geometric aspects of the models in presence and absence of magnetic field are discussed.

17

Some LRS Bianchi Type-II String-Dust Cosmological Models in General Relativity

 

Hassan Amirhashchi and Hishamuddin Zainuddin

 

 

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Some LRS Bianchi type-II string- dust cosmological models are investigated in which the expansion (\theta) is assumed to be proportional to the shear (\sigma). To obtain exact solutions, the Einstein's field equations have been solved for two cases (i) Reddy string and (ii) Nambu string. The physical and geometrical behaviour of these models are discussed.

18

Relativistic Particle Motion and Radiation Reaction in Electrodynamics

 

Richard T. Hammond

 

Full text: Acrobat PDF (423 KB)

 

The problem of radiation reaction and the self force is the oldest unsolved mystery in physics. At times it is considered a minor issue, a malefactor born of classical electrodynamics, while at other times it is public enemy number one, a major inconsistency and unsolved problem. This work derives some of the basic and most important results while reviewing some of the other known approaches to the problem. Some historical notes are given, and yet another approach is discussed that accounts for radiation reaction without the unphysical behavior that plagues so many theories.

19

The Fundamental Equations of Point,  Fluid and Wave Dynamics in the De Sitter-Fantappie-Arcidiacono Projective Relativity Theory

 

Leonardo Chiatti

 

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A review is presented of the fundamental equations of point, perfect incompressible fluid and wave dynamics in the Fantappie-Arcidiacono theory of projective relativity, also known as ``De Sitter relativity''. Compared to the original works, some deductions have been simplified and the physical meaning of the equations has been analyzed in greater depth.

20

Geodesics of Deformed Relativity in Five Dimensions

 

Fabio Cardone, Alessio Marrani and Roberto Mignani

 

Full text: Acrobat PDF (471 KB)

 

In a previous paper, we discussed the Killing symmetries of the Kaluza-Klein-like scheme known as Deformed Relativity in five dimensions (DR5), based on a five-dimensional Riemannian space \mathcal{\Re }_{5} in which the four-dimensional space-time metric is deformed ({i.e.} it depends on the energy) and energy plays the role of the fifth dimension. In the present paper, we carry on the investigation of the main mathematical aspects of DR5 by studying the geodesic motions in \mathcal{\Re }_{5}. In particular, we consider the case of physical relevance in which the metric coefficients are power functions of the energy (Power Ansatz). The geodesic equations are solved explicitly for all the twelve 5-d. metrics obtained as solutions of the vacuum Einstein equations, and in particular for those describing the four fundamental interactions. It is also shown that it is possible, from the geodesic motion related to one of these Power-Ansatz solutions, to get a time-energy uncertainty relation of the Heisenberg type.

21

Theory of Dirac Equation without Negative Energie

 

E. Trubenbacher

 

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It is shown that the well-known Hermitean operator 'sign of frequency' for the free Dirac equation has the physical meaning of 'sign of charge'. Since the kinetic energy of a free particle should not depend on its charge state, this identification requires a modification of the traditional quantum mechanical 4-momentum operators when used with Dirac spinors. Due to the new 4-momentum operators the Dirac equation has no negative energy solutions\textbf{ }and the complex of problems associated with the latter disappears from the theory. The quantum number 'sign of charge' rigorously defines electronic and positronic plane waves. Second quantization of the free Dirac equation does not need the traditional amendments required by the negative energy values. As an example for the application of the theory the relativistic hydrogen ground state wave function is analyzed with respect to the quantum number 'sign of charge'. Since the operator 'sign of charge' does not commute with the Coulomb potential the wave function is only an approximate eigenfunction of  the operator 'sign of charge'. It is shown how one can construct 'effective potentials' that commute with the operator 'sign of charge' and thus are able to produce eigenfunctions of charge when used in the Dirac equation.

                                                                                                           

 

Volume 7, Issue 24 (October 2010)

 

Full text: Acrobat PDF (8,636 KB)

 

Number 

Articles Title

Abstract

1

Editorial Notes

 

Ignazio Licata

 

Full text: Acrobat PDF (21 KB)

 

 

2

Schrödinger's Cat Versus Darwin

 

Z. K. Silagadze

 

Full text: Acrobat PDF (4,638 KB)

 

Sun Wu-k’ung, an immortal Monkey-King of Chaos learns modern physics from the Patriarch Bodhi and questions the Darwinian evolution. He finds that the modern physics indicates towards the intelligent design as a vastly more probably origin of humans than the random evolution by mutations and natural selection.

 

3

Physical Methodology for Economic Systems Modeling

 

I.G. Tuluzov, and S. I. Melnyk

 

Full text: Acrobat PDF (167 KB)

 

The paper discusses the possibility of constructing economic models using the methodology of model construction in classical mechanics. At the same time, unlike the ``econophysical'' approach, the properties of economic models are derived without involvement of any equivalent physical properties, but with account of the types of symmetry existing in the economic system. It has been shown that at this approach practically all known mechanical variables have their ``economic twins''. The variational principle is formulated on the basis of formal mathematical construction without involving the subjective factor common to the majority of models in economics. The dynamics of interaction of two companies has been studies in details, on the basis of which we can proceed to modeling of more complex and realistic economic systems. Prediction of the possibility of constructing economic theory on the basis of primary principles analogously to physics has been made.

 

4

The Study of Markets and Prices

 - The Thermodynamics Approach –

 

S. Prabakaran, and  Khalid Alkhathlan

 

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Many researchers have attempted to viaduct their fields with others to gain insight into their own. In the past decade or so, physicists have begun to do academic research in economics. Perhaps people are now actively involved in an emerging field often called Econophysics. The scope of this paper is to present a phenomenological analysis for Markets and prices with Thermodynamics approach The main ambition of this study is fourfold: 1) First we begin our description of a thermodynamics model of economics with the simplest example. 2) To extend the thermodynamics approach to the study of markets and prices. 3) The problem of the market equilibrium for the two markets with two items of goods. 4) Finally we constructed the economic model with the actual market at constant temperature And this paper end with

conclusion.

 

5

Organization and Complexity in a Nested Hierarchical Spin-Glass like Social Space

 

Fariel Shafee

 

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We lay mathematical foundations for an interaction-based model for multi-agent complex systems.  Emergence and evolution of such systems are analyzed in light of the model.  Various hierarchical levels within such complex systems are observed and the nature of interactions among such levels and among units within the levels are studied.  The modification of the identities of the units is also examined.  Scenarios are briefly mentioned from psychology and social history to suggest possible future uses of the model and to substantiate the need for an interaction-physics based model to understand complex social phenomena.

 

6

Solution to a Problem Found by Calculating the Magnetic Internal Energy Inside Nonextensive Statistical Mechanics

 

Felipe A. Reyes Navarro and Jaime Francisco V. Flores

 

Full text: Acrobat PDF (83 KB)

Herein, in the context of third version of nonextensive statistical mechanics, a theory that generalizes the Boltzmann- Gibbs-Shannon's~statistics, we display a solution for an anomaly found by calculating the internal energy for a composite A+B, of 2 spines 1/2, with additive Hamiltonian H = H_{A}+ H_{B}. Specifically, the calculations of the internal energy in the full Hilbert space is different from the calculations done in the Hilbert subspaces, in other words, $U_{total}$ is different to U_{A} +U_{B}. We carry out analytical calculations. The results exactly indicate that the alternative method of matrices E_{A} and E_{B} is suitable for the calculations of the internal energy. Consequently, the matrix that holds the physical information of the system is {\rho }$^{q}.

 

7

Basins and Critical Curves Generated by A Family of Two-Dimensional Sine Maps

 

Nasr-Eddine Hamri, and Yamina Soula

 

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In this work, we consider a family of two-dimensional coupled sine maps. We provide detailed pictures and some general properties of the associated basin structures, the analysis of the global bifurcations which cause qualitative changes in the shape of chaotic attractors and in the topological structure of the basins is carried out by the method of critical curves. We give the complex phenomena riddled and intermingled basins of attraction. This problem may become particularly challenging when the discrete dynamical system is represented by the iteration of a noninvertible map, because in this case nonconnected or multiply connected basins can be obtained. Coexistence of synchronized and antisynchronized chaotic states [Maistrenko et al., $2005$].

 

8

Propagation of Dust Acoustic Solitary Waves in Saturn F-ring's Region

 

M. I. Abo el Maaty, E. K. El-Shewy, H.G. Abdelwahed, and M. A. Elmessary

 

Full text: Acrobat PDF (1,073 KB)

 

Effect of hot and cold dust charge on the propagation of dust-acoustic waves (DAWs) in unmagnetized plasma having electrons, singly charged ions, hot and cold dust grains have been investigated. The reductive perturbation method is employed to reduce the basic set of fluid equations to the Korteweg-de Vries (KdV) equation. The effect of cold (hot) dusty plasma density n_{c (n_h ) and the charge numbers for negatively charged cold (hot) dust Z_c \;(\;Z_h ) on the nature of DAWs are discussed.

9

Diffeomorphism-Invariant Noncommutative Gravity with Twisted Local Lorentz Invariance

 

Archil Kobakhidze

 

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We propose a new theory of gravitation on noncommutative space-time which is invariant under the general coordinate transformations, while the local Lorentz invariance is realized as twisted gauge symmetry. Our theory is remarkably simpler compared to the existing formulations of noncommutative gravity.

10

Beams Propagation Modelled by Bi-filters

 

B. Lacaze

 

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In acoustic, ultrasonic or electromagnetic propagation, crossed media are often modelled by linear filters with complex gains in accordance with the Beer-Lambert law. This paper addresses the problem of propagation in media where polarization has to be taken into account. Because waves are now bi-dimensional, an unique filter is not sufficient to represent the effects of the medium. We propose a model which uses four linear invariant filters, which allows to take into account exchanges between components of the field. We call it bi-filter because it has two inputs and two outputs. Such a circuit can be fitted to light devices like polarizers, rotators and compensators and to propagation in free space. We give a generalization of the Beer-Lambert law which can be reduced to the usual one in some cases and which justifies the proposed model for propagation of electromagnetic beams in continuous media.

 

11

Effect of Third Order Perturbation on Heisenberg Hamiltonian for Non-Oriented Ultra-Thin Ferromagnetic Films

 

P. Samarasekara, and William A. Mendoza

 

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Third order perturbation of Heisenberg Hamiltonian has been investigated for ultra-thin ferromagnetic films with two and three layers in details. If the second and fourth order anisotropy constants do not vary within the ultra thin film, films with two layers behave as oriented ferromagnetic films. But when the anisotropy constants change within the film, the films indicate non-zero second and third order perturbations. But the films with three layers contribute non-zero second and third order perturbations, even if the second and fourth order anisotropy constants do not vary within the film. The easy and hard directions of sc(001) ultra-thin film with two layers and differed second order anisotropy constants makes 32.4 and 122.4 with film normal, respectively. The main easy and hard directions of sc(001) thin films of three layers with the effect of second order anisotropy are 77 and 167, respectively. After taking fourth order anisotropy into consideration, the positions of maximums and minimums changes. Although the angle between easy and hard directions is not $90^0$, the angle between any two consecutive maximums or minimums is 180 in this case.

 

12

The Modified Dirac Equation

 

B. G. Sidharth

 

Full text: Acrobat PDF (83 KB)

 

 

We consider the behavior of particles at ultra relativistic energies, for both the Klein-Gordon and Dirac equations. We observe that the usual description is valid for energies such that we are outside the particle's Compton wavelength. For higher energies however, both the Klein-Gordon and Dirac equations get modified and this leads to some new effects for the particles, including the appearance of anti particles with a slightly different energy.

13

Non-equilibrium Dynamics as Source of Asymmetries in High Energy Physics

 

Ervin Goldfain

 

Full text: Acrobat PDF (124 KB)

 

 

Understanding the origin of certain symmetry breaking scenarios in high-energy physics remains an open challenge. Here we argue that, at least in some cases, symmetry violation is an effect of non-equilibrium dynamics that is likely to develop somewhere above the energy scale of electroweak interaction. We also find that, imposing Poincaré symmetry in non-equilibrium field theory, leads to fractalization of space-time continuum via period-doubling transition to chaos.

14

A Lie Algebraic Approach to the Schrödinger Equation for Bound States of Pöschl-Teller Potential

 

Subha Gaurab Roy, Joydeep Choudhury, Nirmal Kumar Sarkar, Srinivasa Rao Karumuri and Ramendu Bhattacharjee

 

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The application of Group theoretical techniques to physical problems has a long and fruitful history. Lie algebraic methods have been useful in the study of problems in physics ever since Lie algebras were introduced by M.Sophus Lie (1842-1899) at the end of the 19th century, especially after the development of quantum mechanics. This is because quantum mechanics makes use of commutators [x, P_x]= i\hbar, which are the defining ingredients of Lie algebras. The theory of Lie groups and Lie algebras has become important not only in explaining the behaviour of various physical systems but also in constructing new physical theories. By identifying the suitable Spectrum Generating Algebra (SGA) the problem of interest can be approached. A Spectrum Generating Algebra exists when the Hamiltonian H can be expressed in terms of generators of the algebra. As a consequence the solution of the Schrödinger equation then becomes an algebraic problem which can be attacked using the tools of group theory. Here in this paper we derive the Schrödinger equation for the bound states of Pöschl-Teller potential using Lie algebra.

 

15

Applications of Euclidian Snyder Geometry to the Foundations of Space-Time Physics

 

Andrew Beckwith

 

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The following document is to answer if higher dimensions add value to answering fundamental cosmology questions. The results are mixed, 1^{st} with higher dimensions apparently helping in reconstructing and preserving the value of Planck's constant, and the fine structure constant from a prior to a present universe, while 2^{nd}  failing to add anything different from four dimensional cosmological models to the question of what would cause an increase in the expansion rate of the universe, as of a billion years ago. Finally 3^{rd}, higher dimensions may allow creation of a joint DM and DE model. A choice between LQG and brane world geometry is introduced by Snyder geometry, where Snyder geometry's minimum uncertainty length calculations \Delta x may help determine to what extent gravity is an emergent field that is classical. Independent of the choice of LQG and branes (four dimensions versus higher dimensional cosmology models) is the following question: If gravity is largely classical, how much nonlinearity is involved? Gravitons and their structure as information carriers may help answer these questions. The main point of this document: DM and DE may be unified in terms of cosmological dynamics if the higher dimensional models of DM, as seen by KK towers of gravitons are seen to be pertinent to increasing acceleration of the universe a billion years ago via a 4^{th} dimensional small graviton mass term added to the KK tower DM representation of gravitons (a model of DM).

 

16

On A Riemann-Hilbert Approach to Few Cycle Solitons in Nonlinear Optics

 

Arindam Chakraborty and A. Roy Chowdhury

 

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A new integrable nonlinear equation recently derived in the domain of non linear optics is analysed in the light of Riemann-Hilbert problem. Explicit soliton solutions for the equation are obtained in case of both single and two soliton regimes. Our analysis shows how to use the Riemann-Hilbert procedure with or without utilizing the symmetry of the Lax pair.

17

Positive Energy Projectors and Spinors

 

Tomas Kopf, Jan Kotulek, and Alzbeta Lampartova

 

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In spectral geometry, physical concepts may become a source of geometric data. Here, we examine the vacuum given by a complex structure on phase space. The vacuum provides a soldering form for internal degrees of freedom providing them thus with spatial significance and eventually allowing them to be interpreted as spinors. To show more clearly the possibilities and limitations, the example of a discretized torus is discussed.

18

New Gauge Symmetry in Gravity and the Evanescent Role of Torsion

 

H. Kleinert

 

Full text: Acrobat PDF (1,525 KB)

 

If the Einstein-Hilbert action  \L_\ EH\propto R is re-expressed in Riemann-Cartan spacetime using the gauge fields of translations, the vierbein field  $h^\alpha_\mu$, and the gauge field of local Lorentz transformations, the spin connection A_{\mu \alpha}^ \beta , there exists a new gauge symmetry which permits reshuffling the torsion, partially or totally, into the Cartan curvature term of the Einstein tensor, and back, via a { new multivalued gauge transformation\}. Torsion can be chosen at will by an arbitrary gauge fixing functional. There exist many equivalent ways of specifying the theory, for instance Einstein's traditional way where  L_{EH} is expressed completely  in terms of the metric g_{\mu \nu }=h^ \alpha _\mu h_ \alpha _ \nu , and the torsion is zero, or Einstein's  teleparallel formulation, where  L_{ EH}  is expressed in terms of the torsion tensor, or an infinity of  intermediate ways. As far as the gravitational field in the far-zone of a celestial object is concerned, matter composed of spinning particles can be replaced by matter with only orbital angular momentum, without changing the long-distance forces, no matter which of the various new gauge representations is used.

 

19

Phenomenological Analysis of Hadronic Regge Trajectories

 

Shuchi Bisht, Navjot Hothi, and Gaurav Bhakuni

 

Full text: Acrobat PDF (310 KB)

 

We have analyzed the spectrum of hadrons by the latest data available through the Particle Data Group, with the aim of pinpointing trajectories with which hadronic resonances can be associated. It was recognized that the entire range of Regge trajectories (RTs) for hadrons are not straight and parallel lines. Out of total 66 plotted trajectories, 64.81{\%} are essentially non-linear, 27.78{\%} are essentially linear, while 7.41{\%} are fairly linear. We have extracted a number of inherent parameters of these RTs such as slopes, variance, string tension among quarks and have deduced results which are both in coherence as well as in sharp contrast to the conventional ones. Existence of 15 new resonance particles has been predicted along with some of their intrinsic parameters. The flavor dependence of RTs is also interrogated.

 

20

A Boubaker Polynomials Expansion Scheme Solution to Random Love's Equation in the Case of a Rational Kernel

 

M. Agida, and A. S. Kumar

 

Full text: Acrobat PDF (250 KB)

 

A polynomial expansion scheme is proposed as an analytical method for solving Love's integral equation in the case of a rational kernel. The tangible advantage of the used method, namely the Boubaker polynomials expansion scheme, is the proposition of a piecewise continuous infinitely derivable solution. Comparison with some results proposed in the related literature has been also carried out.

 

21

A Brief Historical Review of the Important Developments in Lanczos Potential Theory

 

P. O'Donnell and H. Pye

 

Full text: Acrobat PDF (136 KB)

 

In this paper we review some of the research that has emerged to form Lanczos potential theory. From Lanczos' pioneering work on quadratic Lagrangians, which ultimately led to the discovery of his famed tensor, through to the current developments in the area of exact solutions of the Weyl—Lanczos equations, we aim to exhibit what are generally considered to be the pivotal advances in the theory.

22

Final State Boundary Condition of Quantum Black Holes at LHC

 

Mohammad Ebrahim Zomorrodian, and Alireza Sepehri

 

Full text: Acrobat PDF (377 KB)

 

 

Final state boundary condition of a system constructed with interacting Dirac field and scalar field near the event horizon of a Schwarzchild metric is analyzed.Also the transformation from the collapsing matter to the state of outgoing Hawking radiation for scalar and dirac fields is calculated. By extending this discussion to mini quantum black holes at LHC the effect of information loss on the average number and cross section of top quarks produced from a single black hole is considered.

23

Rational Galaxy Structure and its Disturbance

 

Jin He

 

 

Full text: Acrobat PDF (662 KB)

 

 

Why is there little dust in elliptical galaxies? Here is a promising answer. Firstly, galaxies are rational. Rationality means that the density distribution of stars is proportional. Secondly, galaxy arms are linearly-shaped and irrational. The presence of arms is the disturbance to the rational disks and bars. Therefore, any disturbance to rational structure produces cosmic dust.

24

A Tilted Homogeneous Cosmological Model with Disordered Radiations and Heat Conduction in Presence of Magnetic Field

 

Anita Bagora

 

Full text: Acrobat PDF (89 KB)

 

 

Investigated homogeneous magnetized cosmological model of perfect fluid distribution having disordered radiation in the presence and absence of magnetic field. To get a determinate solution, we have assumed that the universe is filled with disordered radiation and a supplementary condition is A =(BC)^{n} between metric potentials, n is constant. It has been shown that tilted nature of the model is preserved due to magnetic field. The various physical and geometrical aspects of the model are discussed. The nature of the model in presence and absence of magnetic field is also discussed.

25

Some Bianchi Type IX Stiff Fluid Tilted Cosmological Models with Bulk Viscosity in General Relativity

 

Raj Bali and Pramila Kumawat

 

Full text: Acrobat PDF (101 KB)

 

 

Bianchi type IX stiff fluid tilted cosmological models with bulk viscosity are investigated. To get the deterministic model, we have assumed a supplementary condition A = B^{n} where A and B are metric potentials and n is the constant. The behaviour of the model in presence and absence of bulk viscosity and other physical aspects are also discussed. To get the deterministic solution in terms of cosmic time t, we have also discussed the physical aspects of the model for n = 2.

26

Influence of the Irreducible Triplets on the Velocity Distribution Of Galaxies

 

Farooq Ahmad, Aasifa Nazir, and Manzoor A. Malik

 

Full text: Acrobat PDF (126 KB)

 

 

We derive the velocity distribution function of galaxies from the partition function inclusive of higher order contribution. Our result shows that the effect of higher order contribution on the velocity distribution has an appreciable effect only for small $N$, while for large $N$ the effect is negligible, thus revalidating the earlier results. We also calculate the density of energy states which gives probability for bound and virilized system of galaxies.

27

Some Exact Bianchi Type-V Cosmological Models in Scalar Tensor Theory: Kinematic Tests

 

Anirudh Pradhan, Sheel Kumar Singh

 

Full text: Acrobat PDF (118 KB)

 

 

A new class of a spatially homogeneous and anisotropic Bianchi type-V cosmological models of the universe for perfect fluid distribution within the framework of scalar-tensor theory of gravitation proposed by Saez and Ballester is investigated by applying the law of variation for the generalized mean Hubble's parameter that yields a constant value of deceleration parameter. The variation for Hubble's parameter generates two types of solutions for the average scale factor one is of power-law type and other is of the exponential form. Using these two forms, Einstein's field equations are solved separately that correspond to singular and non-singular models of the universe respectively. It is observed that for positive value of deceleration parameter $q$ of the universe decelerates whereas for negative value of $q$ the universe accelerates. Expressions for look-back time-redshift, neoclassical tests (proper distance $d(z)$), luminosity distance red-shift and event horizon are derived and their significance are described in detail. Some physical and geometrical properties of the models are also discussed.

 

 

Volume 8, Issue 25 (May 2011)

 

Full text: Acrobat PDF (6,123 KB)

 

Number 

Articles Title

Abstract

1

Editorial Notes

 

Ignazio Licata

 

Full text: Acrobat PDF

 

 

2

Bogoliubov's Foresight and Development of the ModernTheoretical Physics

 

A. L. Kuzemsky  

 

 

 

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A brief survey of the author's works on the fundamental conceptual ideas of quantum statistical physics developed by N. N. Bogoliubov and his school was given. The development and applications of the method  of quasiaverages  to quantum statistical physics and condensed matter physics  were  analyzed. The relationship with the concepts of broken symmetry, quantum protectorate and emergence was examined, and the progress to date towards unified understanding of complex many-particle systems was summarized. Current trends for extending and using these ideas in quantum field theory and condensed matter physics were discussed, including microscopic theory of superfluidity and superconductivity, quantum theory of magnetism of complex materials, Bose-Einstein condensation, chirality of molecules, etc.

3

Converting Divergent Weak-Coupling  into Exponentially Fast Convergent Strong-Coupling Expansions

 

Hagen Kleinert

 

 

Full text: Acrobat PDF  

 

 

With the help of a simple variational procedure it is possible to convert the partial sums of order N of many divergent series expansions f(g)=\sum_{n=0}^\infty a_n g^n into partial sums \sum_{n=0}^N b_n g^{- \omega n}, where 0<\omega<1 is a parameter that parametrizes the approach to the large-g limit. The latter are partial sums of a strong-coupling expansion of f(g) which converge against f(g) for $g$ {\em outside\/} a certain divergence radius. The error decreases exponentially fast for large N, like e^{-{\rm const.}\times N^{1-\omega}}. We present a review of the method and various applications.

4

Hubbard-Stratonovich Transformation:Successes, Failure,  and Cure

 

 Hagen Kleinert

 

Full text: Acrobat PDF  

 

 

We recall the successes of the Hubbard-Stratonovich Transformation (HST) of many-body theory, point out its failure to cope with competing channels of collective phenomena and show how to overcome this by Variational Perturbation Theory. That yields exponentially fast converging results, thanks to the help  of a variety of collective classical fields,  rather than a fluctuating collective quantum field as suggested by the HST.

5

A Clarification on the Debate on ``the Original Schwarzschild Solution''

 

Christian Corda

 

Full text: Acrobat PDF

 

Now that English translations of Schwarzschild's original paper exist, that paper has become accessible to more people. Historically, the so-called standard Schwarzschild solution\char` was not the original Schwarzschild's work, but it is actually due to J. Droste and, independently, H. Weyl, while it has been ultimately enabled like correct solution by D. Hilbert. Based on this, there are authors who claim that the work of Hilbert was wrong and that Hilbert's mistake spawned black-holes and the community of theoretical physicists continues to elaborate on this falsehood, with a hostile shouting down of any and all voices challenging them. In this paper we re-analyse the original Schwarzschild solution\char` and we show that it is totally equivalent to the solution enabled by Hilbert. Thus, the authors who claim that the original Schwarzschild solution implies the non existence of black holes give the wrong answer. We realize that the misunderstanding is due to an erroneous interpretation of the different coordinates. In fact, arches of circumference appear to follow the law dl=rd\varphi, if the origin of the coordinate system is a non-dimensional material point in the core of the black-hole, while they do not appear to follow such a law, but to be deformed by the presence of the mass of the central body M if the origin of the coordinate system is the surface of the Schwarzschild sphere.

6

Entropy for Black Holes in the Deformed Horava-Lifshitz Gravity

 

Andres Castillo and Alexis Larra

 

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We study the entropy of black holes in the deformed Horava-Lifshitz gravity with coupling constant \lambda. For \lambda=1, the black hole resembles the Reissner-Nordstrom black hole with a geometric parameter acting like the electric charge. Therefore, we obtain some differences in the entropy when comparing with the Schwarzschild black hole. Finally, we study the heat capacity and the thermodynamical stability of this solution.

7

Canonical Relational Quantum Mechanics from Information Theory

 

Joakim Munkhammar

 

 

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In this paper we construct a theory of quantum mechanics based on Shannon information theory. We define a few principles regarding information-based frames of reference, including explicitly the concept of information covariance, and show how an ensemble of all possible physical states can be setup on the basis of the accessible information in the local frame of reference. In the next step the Bayesian principle of maximum entropy is utilized in order to constrain the dynamics. We then show, with the aid of Lisi's universal action reservoir approach, that the dynamics is equivalent to that of quantum mechanics. Thereby we show that quantum mechanics emerges when classical physics is subject to incomplete information. We also show that the proposed theory is relational and that it in fact is a path integral version of Rovelli's relational quantum mechanics. Furthermore we give a discussion on the relation between the proposed theory and quantum mechanics, in particular the role of observation and correspondence to classical physics is addressed. In addition to this we derive a general form of entropy associated with the information covariance of the local reference frame. Finally we give a discussion and some open problems.

8

On the Logical Origins of Quantum Mechanics Demonstrated By Using Clifford Algebra: A Proof that Quantum Interference Arises in a Clifford Algebraic Formulation of Quantum Mechanics

 

Elio Conte

 

 

 

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We review a rough scheme of quantum mechanics using the Clifford algebra. Following the steps previously published in a paper by another author [31], we demonstrate that quantum interference arises in a Clifford algebraic formulation of quantum mechanics. In 1932 J. von Neumann showed that projection operators and, in particular, quantum density matrices can be interpreted as logical statements. In accord with a previously obtained result by V. F Orlov , in this paper we invert von Neumann's result. Instead of constructing logic from quantum mechanics , we construct quantum mechanics from an extended classical logic. It follows that the origins of the two most fundamental quantum phenomena , the indeterminism and the interference of probabilities, lie not in the traditional physics by itself but in the logical structure as realized here by the Clifford algebra.

9

The Ewald-Oseen Extinction Theorem in the Light of Huygens' Principle

 

Peter Enders

 

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The Ewald-Oseen extinction theorem states, that, inside a linear medium, the incident electromagnetic wave is extinguished by its interference with a part of the irradiation from the excited surface of the medium. This contradicts Huygens' principle, according to which the incident wave is absent after having excited the sources of the secondary wavelets. In this contribution, the proof in Born & Wolf, Optics, is analyzed.

10

Market Fluctuations -- the Thermodynamics Approach

 

 S. Prabakaran

 

 

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A thermodynamic analogy in economics is older than the idea of von Neumann to look for market entropy in liquidity, advice that was not taken in any thermodynamic analogy presented so far in the literature. In this paper, we go further and use a standard approach in market fluctuation and develop a set of equations which are a simple model for market fluctuation in a hypothetical financial market.In the past decade or so, physicists have begun to do academic research in economics. Perhaps people are now actively involved in an emerging field often called Econophysics. The scope of this paper is to present a phenomenological analysis for Market Fluctuations through Thermodynamics approach The main ambition of this study is fourfold:

1) First we begin our description with how market parameters vary with time by using of simplest example. 2) To extend that the market fluctuations appears with the enforced changes of macro parameters of the market and land speculations with non existence.

3) Next we derived the equation for how market fluctuates with respect to time in an equilibrium state.

4) Finally we analyze the how the fluctuations affects the perceptions of the market agents on the future. And this paper end with conclusion.

11

Magnetized Bianchi Type VI_{0} Bulk Viscous Barotropic Massive String Universe with Decaying Vacuum Energy Density \Lambda

 

Anirudh Pradhan  and Suman Lata

 

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Bianchi type VI_{0} bulk viscous massive string cosmological models using the technique given by Letelier (1983) with magnetic field are investigated. To get the deterministic models, we assume that the expansion (\theta) in the model is proportional to the shear ($\sigma$) and also the fluid obeys the barotropic equation of state. The viscosity coefficient of bulk viscous fluid is assumed to be a power function of mass density. The value of the vacuum energy density \Lambda is observed to be small and positive at late time which is supported from recent supernovae Ia observations. The behaviour of the models from physical and geometrical aspects in presence and absence of magnetic field is also discussed.

12

Position Vector Of Biharmonic Curves in the 3-Dimensional Locally \phi-Quasiconformally Symmetric Sasakian Manifold

 

Essin Turhan and Talat Körpinar

 

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In this paper, we study biharmonic curves in locally % \phi -quasiconformally symmetric Sasakian manifold. Firstly, we give some characterizations for curvature and torsion of a biharmonic curve in in locally \phi -quasiconformally symmetric Sasakian manifold. Moreover, we obtain the position vector of biharmonic curve in in locally \phi % -quasiconformally symmetric Sasakian manifold.

13

A Study of the Dirac-Sidharth Equation

 

Raoelina Andriambololona and Christian Rakotonirina

 

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The Dirac-Sidharth equation has been constructed from the Sidharth Hamiltonian by quantification of the energy and momentum in Pauli algebra. We have solved this equation by using tensor product of matrices.

14

Physical Vacuum as the Source of Standard\\ Model Particle Masses

 

C. Quimbay and J. Morales

 

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We present an approach of mass generation for Standard Model particles in which fermions acquire masses from their interactions with physical vacuum and gauge bosons acquire masses from charge fluctuations of vacuum. A remarkable fact of this approach is that left-handed neutrinos are massive because they have a weak charge. We obtain consistently masses of electroweak gauge bosons in terms of fermion masses and running coupling constants of strong, electromagnetic and weak interactions. On the last part of this work we focus our interest to present some consequences of this approach as for instance we first show a restriction about the possible number of fermion families. Next we establish a prediction for top quark mass and finally fix the highest limit for the summing of the square of neutrino masses.

15

Quantum Mechanics as Asymptotics of Solutions of Generalized Kramers Equation

 

E. M. Beniaminov

 

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We consider the process of diffusion scattering of a wave function given on the phase space. In this process the heat diffusion is considered only along momenta. We write down the modified Kramers equation describing this situation. In this model, the usual quantum description arises as asymptotics of this process for large values of resistance of the medium per unit of mass of particle. It is shown that in this case the process passes several stages. During the first short stage, the wave function goes to one of ``stationary'' values. At the second long stage, the wave function varies in the subspace of ``stationary'' states according to the Schrodinger equation. Further, dissipation of the process leads to decoherence, and any superposition of states goes to one of eigenstates of the Hamilton operator. At the last stage, the mixed state of heat equilibrium (the Gibbs state) arises due to the heat influence of the medium and the random transitions among the eigenstates of the Hamilton operator. Besides that, it is shown that, on the contrary, if the resistance of the medium per unit of mass of particle is small, then in the considered model, the density of distribution of probability \rho =|\varphi |^2 satisfies the standard Liouville equation, as in classical statistical mechanics.

16

Application of SU(1,1) Lie algebra in connection with Bound States of Pöschl-Teller Potential

 

Subha Gaurab Roy Raghunandan Das Joydeep Choudhury Nirmal Kumar Sarkar and Ramendu Bhattacharjee

 

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Exactly solvable quantum mechanical potentials have attracted much attention since the early days of quantum mechanics and the Schrödinger equation has been solved for a large number of potentials by employing a variety of methods. Here we consider a specific realization of SU(1,1) algebra and use it to describe the bound states of P\"{o}schl-Teller potential without solving the Schrödinger equation for the mentioned potential.

17

Algebraic Aspects for Two Solvable Potentials

 

Sanjib Meyur

 

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We show that Lie algebras provide us with an useful method for studying real eigenvalues corresponding to eigenfunctions of Hamiltonian. We discuss the SU(2)  Lie algebra. We also discuss the eigenvalues for q-deformed Pöschl-Teller and Scarf potential via Nikiforov-Uvarov method.

18

Bound State Solutions of the Klein Gordon Equation with the Hulthén

Potential

 

Akpan N. Ikot Louis E. Akpabio and Edet J. Uwah

 

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An approximate solution of the Klein--Gordon equation for the Hulthén potential with equal scalar and vector potential is presented. Using the new improved approximation scheme to deal with the centrifugal term, we solve approximately the Klein--Gordon equation via the Nikiforov—Uvarov method for an arbitrary angular momentum quantum number. The corresponding eigen -- energy and eigen functions are also obtained for the s-wave bound state.

19

Chaotic dynamics of the Fractional Order\\ Nonlinear Bloch System

 

Nasr-eddine Hamri and Tarek Houmor

 

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The dynamic behaviors in the fractional-order nonlinear Bloch equations were numerically studied. Basic properties of the system have been analyzed by means of Lyapunov exponents and bifurcation diagrams. The derivative order range used was relatively broad. Regular motions (including period-3 motion) and chaotic motions were examined. The chaotic motion identified was validated by the positive Lyapunov exponent.

20

A Criterion for the Stability Analysis of Phase Synchronization in Coupled Chaotic System

 

Hadi Taghvafard and G. H. Erjaee

 

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We report phase synchronization for the coupled diffusionless Lorenz system and for a new coupled chaotic system in four dimensional space. Stability is also examined by applying a measure to the linearlized evaluation difference matrix between coupled chaotic systems.

21

Synchronization of Different Chaotic Fractional-Order Systems via Approached Auxiliary System the Modified Chua Oscillator and the Modified Van der Pol-Duffing Oscillator

 

T. Menacer and N. Hamri

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In this paper we propose the study of synchronization between two different chaotic fractional-order systems via approached auxiliary system, we choose the modified Chua oscillators as a master system and the modified Van der Pol-Duffing oscillator (MVDPD) as a slave system, this method is also detected for both well known systems Chen and Lu. Routh- Hurwitz criterion is used for the study of stability of error system between the master-slave systems. Numerical results show the effectiveness of the theoretical analysis.

22

A Universal Nonlinear Control Law for the Synchronization of Arbitrary 4-D\Continuous-Time Quadratic Systems

 

Zeraoulia Elhadj and J. C. Sprott

 

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In this letter we show the existence of a universal nonlinear control law (without any conditions) for the synchronization of arbitrary 4-D continuous-time quadratic systems.

23

On a General Class of Solutions of a Nonholonomic Extension of Optical Pulse Equation

 

Pinaki Patra, Arindam  Chakraborty and A. Roy Chowdhury

 

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A Nonholonomic extension of an equation obeyed by short pulse in non-linear optics is obtained. A general class of solutions of such an equation is obtained with the help of Riemann-Hilbert technique.

24

Schwinger Mechanism for Quark-Antiquark Production in the Presence of Arbitrary Time Dependent Chromo-Electric Field

 

Gouranga C. Nayak

 

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We study the Schwinger mechanism in QCD in the presence of an arbitrary time-dependent chromo-electric background field E^a(t) with arbitrary color index a=1,2,...8 in SU(3).We obtain an exact result for the non-perturbative quark (antiquark) production from an arbitrary E^a(t) by directly evaluating the path integral. We find that the exact result is independent of all the time derivatives \frac{d^nE^a(t)}{dt^n} where n=1,2,...\infty. This result has the same functional dependence on two Casimir invariants $[E^a(t)E^a(t)]$ and [d_{abc}E^a(t)E^b(t)E^c(t)]^2 as the constant chromo-electric field $E^a$ result with the replacement: E^a \rightarrow E^a(t). This result relies crucially on the validity of the shift conjecture, which has not yet been established.

25

Relic Universe

 

M. Kozlowski and J. Marciak-Kozlowska

 

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In this paper we present the anthropic model calculation of the contemporary Universe. The values of the radius Universe, velocity of expansion and acceleration are calculated. In addition the cosmological parameter Lambda in de Sitter Universe is calculated. We argue that the present Epoch Universe is the Relic Universe. The future of the Universe is diagnosed and discussed.

26

Halo Spacetime

 

Mark D. Roberts

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It is shown that constant galactic rotation curves require a logarithmic potential in both Newtonian and relativistic theory. In Newtonian theory the density vanishes asymptotically, but there are a variety of possibilities for perfect fluid Einstein theory.

27

C-field Barotropic Fluid Cosmological Model with Variable G in FRW space-time

 

Raj Bali and Meghna Kumawat

 

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C-field cosmological model with variable G for barotropic perfect fluid distribution in flat FRW (Friedmann-Robertson-Walker) space-time is investigated. To get the deterministic model of the universe, we assume that G = R^{n} where R is scale factor and n is a constant. We find that the creation field (C) increases with time, G and \rho (matter density) decreases with time and \frac{\dot {G}}{G}={H(t)} where H is the Hubble parameter. These results match with the observations.

28

Two-Fluid Cosmological Models in Bianchi Type-III Space-Time

 

K. S. Adhav S. M. Borikar, M. S. Desale, and R. B. Raut

 

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In this paper we have studied anisotropic, homogeneous two-fluid cosmological models in a Bianchi type III space-time. Here one fluid represents the matter content of the universe and another fluid is chosen to model the CMB radiation. These cosmological models depict two different scenarios of cosmic history i.e. one when the radiation and matter content of the universe are in interactive phase and another when the two are in non-interacting phase.

29

Shell Closures and Structural Information from Nucleon Separation Energies

 

 C. Anu Radha V. Ramasubramanian and E. James Jebaseelan Samuel

 

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In this work nuclei along N=Z line are of interest as transitions from spherical to deformed shapes are expected to occur when going across the medium mass region. In this respect a strong sudden shape transition between deformation is predicted to occur in the region N=Z as well as N$>$Z nuclei. New shell gaps are predicted using nucleon and two-nucleon separation energies and the shape evaluation are depicted by applying triaxially deformed cranked Nilsson Strutinsky calculations. Nucleon separation energy plays a major role in the prediction of new magicity in the proton and neutron drip line nuclei.

30

Calculating Vacuum Energy as a Possible Explanation of the Dark Energy

 

B. Pan

 

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We carried out a study of the properties of the \lambda \phi^4 field solutions. By constructing Gaussian wave packets to calculate the $S$ matrix, we show that the probability of the vacuum unbroken state transfers to the broken state is about 10^{-52}. After adding this probability restriction condition as modulation factor in the summation of vacuum energy, we thus get a result that the vacuum energy density is about 10^{-47}GeV^4, which is exact same as the observed dark energy density value, and maybe served as a possible explanation of the dark energy. Also our result shows that the vacuum energy density is proportional to the square of the universe's age, which fits the Dirac large numbers hypothesis.

31

Some Bianchi type-I Cosmic Strings in a Scalar --Tensor Theory of Gravitation

 

R.Venkateswarlu, J.Satish and K.Pavan Kumar

 

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The field equations are obtained in Sen--Dunn theory of gravitation with the help of LRS Bainchi type-I in the context of cosmic strings. We have solved the field equations when the shear \sigma  is proportional to the scalar expansion \ theta. It is found that the cosmic do not exist with the scalar field except for some special cases and hence vacuum solutions are presented and discussed.

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Gravitons Writ Large; I.E. Stability, Contributions to Early Arrow of Time, and Also Their Possible Role in Re Acceleration of the Universe 1 Billion Years Ago?

 

A. Beckwith

 

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This document is due to a question by Debasish of the Saha institute of India asked in the Dark Side of the Universe conference, 2010, in Leon, Mexico, and also is connected with issues as to the initial configuration of the arrow of time brought up in both Rudn 10, in Rencontres de Blois, and Fundamental Frontiers of Physics 11, in Paris, in July 2010. Further reference is made as to how to reconcile early inflation with re acceleration, partly by dimensional analysis and partly due to recounting a suggestion as by Yurov, which the author thinks has merit and which ties into, to a point with using massive gravitons as a re acceleration of the universe a billion years ago enabler, as perhaps a variant of DE.

33

Dimensionless Constants and Blackbody Radiation Laws

 

Ke Xiao

 

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The fine structure constant \alpha= {e}^{2}/\hbar c\approx1/137.036 and the blackbody radiation  constant \alpha_{R}={e}^{2}(a_{R}/k_{B}^{4})^{1/3} \approx1/157.555 are two dimensionless constants, derived respectively from a  discrete  atomic spectra and a continuous  radiation spectra and linked by an infinite prime product. The blackbody radiation constant governs large density matter where oscillating charges emit or absorb photons that obey the Bose-Einstein statistics. The new derivations of Planck's law, the Stefan-Boltzmann law, and Wein's displacement law are based on the fine structure constant and a simple 3D interface model. The blackbody radiation constant provides a new method to measure the fine structure constant and links the fine structure constant to the Boltzmann constant.

                                                                                                           

 

 

 

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