Electronic Journal of Theoretical Physics Open access journal for theoretical physics

# Volume 2, Issue 7 (August 2005)

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# Volume 2, Issue 8 (December 2005)

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 Number Articles Title Abstract 1 Fractional Unstable Euclidean Universe.    El-Nabulsi Ahmad Rami   Full text: Acrobat PDF (174 KB) 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   Full text: Acrobat PDF (153 KB) 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     Full text: Acrobat PDF (326 KB) 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   Full text: Acrobat PDF (203 KB) 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   Full text: Acrobat PDF (132 KB) 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     Full text: Acrobat PDF (335 KB) 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.       Full text: Acrobat PDF (403 KB) 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   Full text: Acrobat PDF (465 KB) 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   Full text: Acrobat PDF (110 KB) 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   Full text: Acrobat PDF (168 KB) 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         Full text: Acrobat PDF (292 KB) 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   Full text: Acrobat PDF (14 KB) Editorial Note 1 The Scientific Work Of Ettore Majorana: An Introduction   Erasmo Recami   Full text: Acrobat PDF (113 KB) 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   Full text: Acrobat PDF (126 KB) 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   Full text: Acrobat PDF (199 KB) 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   Full text: Acrobat PDF (131 KB) 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   Full text: Acrobat PDF (346 KB) 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   Full text: Acrobat PDF (161 KB) 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   Full text: Acrobat PDF (218 KB) 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   Full text: Acrobat PDF (143 KB) 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   Full text: Acrobat PDF (400 KB) 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   Full text: Acrobat PDF (287 KB) 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   Full text: Acrobat PDF (380 KB) 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   Full text: Acrobat PDF (162 KB) 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   Full text: Acrobat PDF (169 KB) 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   Full text: Acrobat PDF (215 KB) 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     Full text: Acrobat PDF (161 KB) 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   Full text: Acrobat PDF (219 KB) 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     Full text: Acrobat PDF (124 KB) 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     Full text: Acrobat PDF (166 KB) 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     Full text: Acrobat PDF (145 KB) 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)

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# 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   Full text: Acrobat PDF (222 KB) 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     Full text: Acrobat PDF (335 KB) 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     Full text: Acrobat PDF (135 KB) 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   Full text: Acrobat PDF (163 KB) 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     Full text: Acrobat PDF (118 KB) 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   Full text: Acrobat PDF (159 KB) 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     Full text: Acrobat PDF (96 KB) 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   Full text: Acrobat PDF (253 KB) 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   Full text: Acrobat PDF (204 KB) 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   Full text: Acrobat PDF (342 KB) 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   Full text: Acrobat PDF (227 KB) 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   Full text: Acrobat PDF (125 KB) 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     Full text: Acrobat PDF (166 KB) 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     Full text: Acrobat PDF (124 KB) 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     Full text: Acrobat PDF (166 KB) 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   Full text: Acrobat PDF (193 KB) 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     Full text: Acrobat PDF (193 KB) 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   Full text: Acrobat PDF (186 KB) 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     Full text: Acrobat PDF (267 KB) 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   Full text: Acrobat PDF (250 KB) 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   Full text: Acrobat PDF (136 KB) 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   Full text: Acrobat PDF (123 KB) 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   Full text: Acrobat PDF (136 KB) 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   Full text: Acrobat PDF (130 KB) 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   Full text: Acrobat PDF (174 KB) 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   Full text: Acrobat PDF (152 KB) 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   Full text: Acrobat PDF (385 KB) 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   Full text: Acrobat PDF (157 KB) 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   Full text: Acrobat PDF (130 KB) 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   Full text: Acrobat PDF (197 KB) 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   Full text: Acrobat PDF (297 KB) 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   Full text: Acrobat PDF (124 KB) 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)

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# Volume 8, Issue 25 (May 2011)

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 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         Full text: Acrobat PDF 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   Full text: Acrobat PDF 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     Full text: Acrobat PDF 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       Full text: Acrobat PDF 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   Full text: Acrobat PDF 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     Full text: Acrobat PDF 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   Full text: Acrobat PDF 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   Full text: Acrobat PDF 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   Full text: Acrobat PDF 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   Full text: Acrobat PDF 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   Full text: Acrobat PDF 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   Full text: Acrobat PDF 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   Full text: Acrobat PDF 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   Full text: Acrobat PDF 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   Full text: Acrobat PDF 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   Full text: Acrobat PDF 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 Full text: Acrobat PDF 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   Full text: Acrobat PDF 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   Full text: Acrobat PDF 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   Full text: Acrobat PDF 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   Full text: Acrobat PDF 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 Full text: Acrobat PDF 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   Full text: Acrobat PDF 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   Full text: Acrobat PDF 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   Full text: Acrobat PDF 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   Full text: Acrobat PDF 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   Full text: Acrobat PDF 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. 32 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   Full text: Acrobat PDF 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   Full text: Acrobat PDF 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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