Electronic Journal of Theoretical Physics

Open access journal for theoretical physics

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 Full text: Acrobat PDF (197 KB)	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 Full text: Acrobat PDF (126 KB)	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 Full text: Acrobat PDF (139 KB)	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 Full text: Acrobat PDF (249 KB)	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 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

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Editorial Note

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.

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.

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.

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.

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.

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.

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.

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.

" 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.

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.

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.

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.

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.

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.

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.

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.

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’.

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

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.

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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Number

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Abstract

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.

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.

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.

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.

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.

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.

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.

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]).

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.

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.

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.

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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Abstract

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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 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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Number	Articles Title	Abstract
1	*Mental and Physical Objects in Quantum Mechanics:Any Lessons for Other Disciplines?* M. Cini Full text: Acrobat PDF (126 KB)	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 Full text: Acrobat PDF (183 KB)	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 Full text: Acrobat PDF (143 KB)	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 Full text: Acrobat PDF (141 KB)	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 Full text: Acrobat PDF (77 KB)	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 Full text: Acrobat PDF (185 KB)	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 Full text: Acrobat PDF (131 KB)	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 Full text: Acrobat PDF (65 KB)	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 Full text: Acrobat PDF (305 KB)	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 Full text: Acrobat PDF (155 KB)	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 Full text: Acrobat PDF (119 KB)	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 Full text: Acrobat PDF (580 KB)	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 Full text: Acrobat PDF (104 KB)	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 Full text: Acrobat PDF (147 KB)	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 16II ( December 2007)

Full text: Acrobat PDF (2,452 KB)

Number	Articles Title	Abstract
1	*The Limits of Atomism, the Bohm Way of a New Ontology* Ryo Morikawa Full text: Acrobat PDF (107 KB)	In this paper, we survey a developed outline of atomism. The paper clarifies that this leading principle of modern physics faces a limitation. This limitation is a limit of ontology. We are unable to recognize a concrete ontology; we have only epistemology. Therefore, we discuss this issue from a philosophical viewpoint by referring to Cassirer's philosophy. These arguments will clarify that there is a need for a new ontology that will be able to make a consistent understanding from the microscopic to the macroscopic level. To do this we argue the case of the new ontology that was introduced by Bohm. Also, we will see the mathematical formalism of cyclic ontology as a new ontology for the process. Then we will see that this formalism is able to obtain the Heisenberg equation as well as the Bohm equation.
2	*Physics of Life from First Principles* Michail Zak Full text: Acrobat PDF (562 KB)	The objective of this work is to extend the First Principles of Newtonian mechanics to include modeling of behavior of Livings. One of the most fundamental problems associated with modeling life is to understand a mechanism of progressive evolution of complexity typical for living systems. It has been recently recognized that the evolution of living systems is progressive in a sense that it is directed to the highest levels of complexity if the complexity is measured by an irreducible number of different parts that interact in a well-regulated fashion. Such a property is not consistent with the behavior of isolated Newtonian systems that cannot increase their complexity without external forces. Indeed, the solutions to the models based upon dissipative Newtonian dynamics eventually approach attractors where the evolution stops, while these attractors dwell on the subspaces of lower dimensionality, and therefore, of the lower complexity. If thermal forces are added to mechanical ones, the Newtonian dynamics is extended to the Langevin dynamics combining both mechanics and thermodynamics effects; it is represented by stochastic differential equations that can be utilized for more advanced models in which randomness stands for multi-choice patterns of behavior typical for living systems. However, even those models do not capture the main property of living systems, i.e. their ability to evolve towards increase of complexity without external forces. Indeed, the Langevin dynamics is complemented by the corresponding diffusion equation that describes the evolution of the distribution of the probability density over the state variables; in case of an isolated system, the entropy of the probability density cannot decrease, and that expresses the second law of thermodynamics. From the viewpoint of complexity, this means that the state variables of the underlying system eventually start behaving in a uniform fashion with lesser distinguished features, i.e. with lower complexity. Reconciliation of evolution of life with the second law of thermodynamics is the central problem addressed in this paper. It is solved via introduction of the First Principle for modeling behavior of living systems. The structure of the model is quantum-inspired: it acquires the topology of the Madelung equation in which the quantum potential is replaced with the information potential. As a result, the model captures the most fundamental property of life: the progressive evolution, i.e. the ability to evolve from disorder to order without any external interference. The mathematical structure of the model can be obtained from the Newtonian equations of motion (representing the motor dynamics) coupled with the corresponding Liouville equation (representing the mental dynamics) via information forces. The unlimited capacity for increase of complexity is provided by interaction of the system with its mental images via chains of reflections: What do you think I think you think?. All these specific non-Newtonian properties equip the model with the levels of complexity that match the complexity of life, and that makes the model applicable for description of behaviors of ecological, social and economics systems.
3	*Theoretical Physics of DNA: New Ideas and Tendencies in the Modeling of the DNA Nonlinear Dynamics* Yakushevich L.V. Full text: Acrobat PDF (254 KB)	Theoretical studies of the DNA nonlinear dynamics successfully started with the model of Englander [1] in 1980, was intensively developed at the end of the 20th century. Most of the proposed models and results obtained have been summarized in the reviews [2-5] and books [6-9]. And what was happened after that? What new ideas, results and tendencies one can observe in this field of science now? Here we describe some of them.
4	*Mathematical and Data Mining Contributions to Dynamics and Optimization of Gene-Environment Networks* Gerhard-Wilhelm Weber, Pakize Taylan , Başak Akteke-Őztürka, and Őmür Uğur Full text: Acrobat PDF (255 KB)	This paper further introduces continuous optimization into the fields of computational biology and environmental protection which belong to the most challenging and emerging areas of science. It refines earlier ones of our models on gene-environment patterns by the use of optimization theory. We emphasize that it bases on and presents work done in ougur, weber-et-al.. Furthermore, our paper tries to detect and overcome some structural frontiers of our methods applied to the recently introduced {\it gene-environment networks}. Based on the experimental data, we investigate the ordinary differential equations having nonlinearities on the right-hand side and a generalized treatment of the absolute shift term which represents the environmental effects. The genetic process is studied by a time-discretization, in particular, Runge-Kutta type discretization. The possibility of detecting stability and instability regions is being shown by a utilization of the combinatorial algorithm of Brayton and Tong which is based on the orbits of polyhedra. The time-continuous and discrete systems can be represented by means of matrices allowing biological implications, they encode and are motivated by our gene-environment networks. A specific contribution of this paper consists in a careful but rigorous integration of the environment into modeling and dynamics, and in further new sights. Relations to parameter estimation within modeling, especially, by using optimization, are indicated, and future research is addressed, especially towards the use of stochastic differential equations. This practically motivated and theoretically elaborated work is devoted for a contribution to better health care, progress in medicine, a better education and more healthy living conditions recommended.
5	*Folding Proteins:(How to Set up an Effcient Metrics for Dealing with Complex Systems)* Alessandro Giuliani Full text: Acrobat PDF (173 KB)	Protein folding, the process allowing a monodimensional string of aminoacids to acquire its characteristic shape in solution, is where complexity starts, as clearly stated in a famous paper entitled `Proteins: where physics of simplicity and complexity meet' by Hans Frauenfelder and Peter Wolynes [1]. The starting of complexity implies the coupling of a thorough and accurate knowledge of the `first principles' and potentials (hydrophobic interactions, hydrogen bonding, size constraints etc.) acting at the microscopic level with the substantially empirical (and very inaccurate) predictions on the actual structure of proteins when in solution. Along the pilgrimage to the `translation key' from protein sequence to structure, scientists of different cultures have met and exchanged ideas and, as often happens to pilgrims, even the nature of the goal changed along the way. This is a tale from a section of this path (still very far to be completed) in which some peculiarities of the network based formalization of protein sequence and structure are presented as an example of a possible way to generate an efficient metrics to study phenomena in which many different actors interact in a complex way.
6	*Evolution of Norms in a Multi-Level Selection Model of Conflict and Cooperation* J. M. Pacheco, F. C. Santos and F. A. C. C. Chalub Full text: Acrobat PDF (356 KB)	We investigate the evolution of social norms in a game theoretical model of multi-level selection and mutation. Cooperation is modeled at the lower level of selection by means of a social dilemma in the context of indirect reciprocity, whereas at the higher level of selection conflict is introduced via different mechanisms. The model allows the emergence of norms requiring high levels of cognition. Results show that natural selection and mutation lead to the emergence of a robust yet simple social norm, which we call stern-judging. Stern-judging is compatible with expectations that anthropologists have regarding the Pleistocene hunter gatherer communities. Perhaps surprisingly, it also fits very well recent studies of the behavior of reputation-based e-trading. Under stern-judging, helping a good individual or refusing help to a bad individual leads to a good reputation, whereas refusing help to a good individual or helping a bad one leads to a bad reputation. The lack of ambiguity of stern-judging, where implacable punishment is compensated by prompt forgiving, supports the idea that simplicity is often associated with evolutionary success.
7	*Multiboundary Algebra as Pregeometry* Ben Goertzel Full text: Acrobat PDF (96 KB)	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.
8	*Scale Relativity: A Fractal Matrix for Organization in Nature* Laurent Nottale Full text: Acrobat PDF (570 KB)	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.
9	*Fractal Time, Observer Perspectives and Levels of Description in Nature* Susie Vrobel Full text: Acrobat PDF (327 KB)	This paper reviews various approaches to modeling reality by differentiating notions of time which underly those models. Basic notions of time presupposed in physical theories are briefly described and analyzed in terms of the levels of description taken into account, the interfacial cut assumed between the observer and the rest of the world, the resulting observer perspectives and the extent to which these notions are based on temporal natural constraints. Notions of time in physical theories are secondary constructs, derived from our primary experiences of time. Therefore, we must regard our theories as anthropocentric -- derived from abstractions and metaphors resulting from our embodied cognition. Theories based on the notion of fractal time and fractal space-time are generalizations or alternative descriptions which allow for a more differentiated modelling of reality. The resulting temporal observer perspectives allow for further differentiation. The notion of fractal time logically precedes those of fractal space-time, as it is based on the primary experiences of time: succession, simultaneity, duration and an extended Now. Against this background, the internal differentiation of the observer and his degree of both conscious and unconscious contextualization turn out to be vital ingredients in our reality generation game. I am fully aware of the fact that the selection of concepts presented here is neither complete nor unbiased and is coloured by my own temporal observer perspective.

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 Full text: Acrobat PDF (649 KB)	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 Full text: Acrobat PDF (165 KB)	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 Full text: Acrobat PDF (177 KB)	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 Full text: Acrobat PDF (210 KB)	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 Full text: Acrobat PDF (126 KB)	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 Full text: Acrobat PDF (195 KB)	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 Full text: Acrobat PDF (174 KB)	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 Full text: Acrobat PDF (136 KB)	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 Full text: Acrobat PDF (638 KB)	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 Full text: Acrobat PDF (159 KB)	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* Full text: Acrobat PDF (256 KB)	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 Full text: Acrobat PDF (239 KB)	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 Full text: Acrobat PDF (242 KB)	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 Full text: Acrobat PDF (175 KB)	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 Full text: Acrobat PDF (137 KB)	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 Full text: Acrobat PDF (187 KB)	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 Full text: Acrobat PDF (197 KB)	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 Full text: Acrobat PDF (467 KB)	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 Full text: Acrobat PDF (124 KB)	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 Full text: Acrobat PDF (178 KB)	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 Full text: Acrobat PDF (125 KB)	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 Full text: Acrobat PDF (83 KB)	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 Full text: Acrobat PDF (128 KB)	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 Full text: Acrobat PDF (131 KB)	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 Full text: Acrobat PDF (218 KB)	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 Full text: Acrobat PDF (116 KB)	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 Full text: Acrobat PDF (104 KB)	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 Full text: Acrobat PDF (150 KB)	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. Full text: Acrobat PDF (98 KB)	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 Full text: Acrobat PDF (94 KB)	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 Full text: Acrobat PDF (145 KB)	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 Full text: Acrobat PDF (124 KB)	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 Full text: Acrobat PDF (124 KB)	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 Full text: Acrobat PDF (103 KB)	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 Full text: Acrobat PDF (102 KB)	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 Full text: Acrobat PDF (97 KB)	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 Full text: Acrobat PDF (101 KB)	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 Full text: Acrobat PDF (306 KB)	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 Full text: Acrobat PDF (169 KB)	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 Full text: Acrobat PDF (209 KB)	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 Full text: Acrobat PDF (281 KB)	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 Full text: Acrobat PDF (742 KB)	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