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A. E. Shalyt-Margolin

Publications and source records attributed to A. E. Shalyt-Margolin.

At least 19 recordsLinked to original sources
arXiv2016

Minimal Length, Measurability and Gravity

The present work is a continuation of the previous papers written by the author on the subject. In terms of the measurability (or measurable quantities) notion introduced in a minimal length theory, first the consideration is given to a quantum theory in the momentum representation. The same terms are used to consider the Markov gravity model that here illustrates the general approach to studies of gravity in terms of measurable quantities. This paper is dedicated to the 75th Anniversary of Professor Vladimir Grigor'evich Baryshevsky.

gr-qc↗
arXiv2014

Minimal Length and the Existence of Some Infinitesimal Quantities in Quantum Theory and Gravity

In this work it is demonstrated that, provided a theory involves a minimal length, this theory must be free from such infinitesimal quantities as infinitely small variations in surface of the holographic screen, its volume, and entropy. The corresponding infinitesimal quantities in this case must be replaced by the "minimal variations possible" -- finite quantities dependent on the existent energies. As a result, the initial low-energy theory (quantum theory or general relativity) inevitably must be replaced by a minimal-length theory that gives very close results but operates with absolutely other mathematical apparatus.

physics.gen-ph↗
arXiv2013

Spacetime Quantum Fluctuations, Minimal Length and Einstein Equations

In the process of work it has been found that space-time quantum fluctuations are naturally described in terms of the deformation parameter introduced on going from the well-known quantum mechanics to that at Planck scales and put forward in the previous works of the author. As shown, with the use of quite natural assumptions, these fluctuations must be allowed for in Einstein Equations to lead to the dependence of the latter on the above-mentioned parameter, that is insignificant and may be ignored at low energies but is of particular importance at high energies. Besides, some inferences form the obtained results are maid.

physics.gen-ph↗
arXiv2013

The Black Hole Quantum Entropy and Its Minimal Value

In the paper it is demonstrated that the Schwarzschild black-hole quantum entropy computed within the scope of the Generalized Uncertainty Principle has a nonzero minimum under the assumption that for a radius of the black hole the lower limit is placed, whose value is twice the minimal length. Such a limit is quite natural when using, as a proper deformation parameter in a quantum theory with a minimal length, the dimensionless small parameter introduced previously by one of the authors in co-authorship with his colleagues and caused by modification of the density matrix at Planck scales. The results obtained have been compared to the results of other authors and analyzed from the viewpoint of their compatibility with the well-known facts and the holographic principle in particular.

physics.gen-ph↗
arXiv2012

Quantum Theory at Planck Scale, Limiting Values, Deformed Gravity and Dark Energy Problem

Within a theory of the existing fundamental length on the order of Planck's a high-energy deformation of the General Relativity for the space with horizon has been constructed. On this basis, Markov's work of the early eighties of the last century has been given a new interpretation to show that the heuristic model considered by him may be placed on a fundamental footing. The obtained results have been applied to solving of the dark energy problem, making it possible to frame the following hypothesis: a dynamic cosmological term is a measure of deviation from a thermodynamic identity (the first law of thermodynamics) of the high-energy (Planck's) deformation of Einstein equations for horizon spaces in their thermodynamic interpretation.

gr-qc↗
arXiv2010

Deformed Quantum Field Theory, Thermodynamics at Low and High Energies, and Gravity. II. Deformation Parameter

This work is a continuation of studies presented in the papers arXiv:0911.5597, arXiv:1003.4523. In the work it is demonstrated that with the use of one and the same parameter deformation may be described for several cases of the General Relativity within the scope of both the Generalized Uncertainty Principle (UV-cutoff) and the Extended Uncertainty Principle (IR-cutoff). All these cases have a common thermodynamic interpretation of the corresponding gravitational equations. Consideration is given to the possibility for extension of the obtained results to more general cases. Possible generalization of the uncertainty relation for the pair (cosmological constant, "space-time volume"), where the cosmological constant is regarded as a dynamic quantity at high and low energies is analyzed.

gr-qc↗
arXiv2010

Entropy In The Present And Early Universe: New Small Parameters And Dark Energy Problem

It is demonstrated that entropy and its density play a significant role in solving the problem of the vacuum energy density (cosmological constant) of the Universe and hence the dark energy problem. Taking this in mind, two most popular models for dark energy - Holographic Dark Energy Model and Agegraphic Dark Energy Model - are analyzed. It is shown that the fundamental quantities in the first of these models may be expressed in terms of a new small dimensionless parameter. It is revealed that this parameter is naturally occurring in High Energy Gravitational Thermodynamics and Gravitational Holography (UV-limit). On this basis the possibility of a new approach to the problem of Quantum Gravity is discussed. Besides, the results obtained on the uncertainty relation of the pair "cosmological constant - volume of space-time", where the cosmological constant is a dynamic quantity, are reconsidered and generalized up to the Generalized Uncertainty Relation.

gr-qc↗
arXiv2010

Deformed Quantum Field Theory, Thermodynamics at Low and High Energies, and Gravity. I

The present work is a natural continuation of the previous paper arXiv:0911.5597. In this work, within the scope of the Generalized Uncertainty Principle, a model of the high energy deformation for a particular case of Einstein's equations is developed. In the process a thermodynamic description of General Relativity is used. And the deformation is understood as an extension of a particular theory by inclusion of one or several additional parameters in such a way that the initial theory appears in the limiting transition. The possibility for the high energy deformation of Einstein's equations within the scope of both equilibrium thermodynamics and non-equilibrium thermodynamics is examined

hep-th↗
arXiv2007

Vacuum Energy Problem, Fundamental Length and Deformed Quantum Field Theory

The cosmological constant (vacuum energy) problem is analyzed within the scope of quantum theories with UV-cut-off or fundamental length. Various cases associated with the appearance of the latter are considered both using the Generalized Uncertainty Relations and the deformed density matrix,previously introduced in the author's works. The use of the deformed density matrix is examined in detail. It is demonstrated that, provided the Fischler-Susskind cosmic holographic conjecture is valid, the Vacuum Energy Density takes a value close to the experimental one. The arguments supporting the validity of this conjecture are given on the basis of the recently obtained results on Gravitational Holography.

gr-qc↗
arXiv2007

Application of Geometric Phase in Quantum Computations

Geometric phase that manifests itself in number of optic and nuclear experiments is shown to be a useful tool for realization of quantum computations in so called holonomic quantum computer model (HQCM). This model is considered as an externally driven quantum system with adiabatic evolution law and finite number of the energy levels. The corresponding evolution operators represent quantum gates of HQCM. The explicit expression for the gates is derived both for one-qubit and for multi-qubit quantum gates as Abelian and non-Abelian geometric phases provided the energy levels to be time-independent or in other words for rotational adiabatic evolution of the system. Application of non-adiabatic geometric-like phases in quantum computations is also discussed for a Caldeira-Legett-type model (one-qubit gates) and for the spin 3/2 quadrupole NMR model (two-qubit gates). Generic quantum gates for these two models are derived. The possibility of construction of the universal quantum gates in both cases is shown.

quant-ph↗
arXiv2006

The Holographic Principle and Dark Energy. I.Deformed Quantum Field Theory and New Small Parameters

In this work the Vacuum Energy Density Problem or Dark Energy Problem is studied on the basis of the earlier results by the author within the scope of the Holographic Principle. It is demonstrated that the previously introduced deformed quantum field theory at a nonuniform lattice in the finite-dimensional hypercube is consistent with the Holographic Principle (Holographic Entropy Bound)in case the condition of the physical system's stability with respect to the gravitational collapse is met, or simply stated, the gravitational stability is constrained. The associated deformation parameter is the basic characteristic, in terms of which one can explain the essence of such a quantity as the vacuum energy density and its smallness. Moreover, the entropy characteristics are also well explained in terms of the above deformation parameter. The relation of this work to other studies devoted to the Dark Energy Problem is considered. Besides, the principal problems (tasks) are formulated; both the well-known problems and those naturally following from the obtained results

hep-th↗
arXiv2006

Deformed Density Matrix and Quantum Entropy of the Black Hole

In the present work the approach - density matrix deformation - earlier developed by the author to study a quantum theory of the Early Universe (Planck's scales) is applied to study a quantum theory of black holes. On this basis the author investigates the information paradox problem, entropy of the black hole remainders after evaporation, and consistency with the holographic principle. The possibility for application of the proposed approach to the calculation of quantum entropy of a black hole is considered.

gr-qc↗
arXiv2004

The Universe as a Nonuniform Lattice in the Finite-Dimensional Hypercube II.Simple Cases of Symmetry Breakdown and Restoration

This paper continues a study of field theories specified for the nonuniform lattice in the finite-dimensional hypercube with the use of the earlier described deformation parameters. The paper is devoted to spontaneous breakdown and restoration of symmetry in simple quantum-field theories with scalar fields. It is demonstrated that an appropriate deformation opens up new possibilities for symmetry breakdown and restoration. To illustrate, at low energies it offers high-accuracy reproducibility of the same results as with a nondeformed theory. In case of transition from low to higher energies and vice versa it gives description for new types of symmetry breakdown and restoration depending on the rate of the deformation parameter variation in time, and indicates the critical points of the previously described lattice associated with a symmetry restoration. Besides, such a deformation enables one to find important constraints on the initial model parameters having an explicit physical meaning.

hep-th↗
arXiv2004

Pure States, Mixed States and Hawking Problem in Generalized Quantum Mechanics

This paper is the continuation of a study into the information paradox problem started by the author in his earlier works. As previously, the key instrument is a deformed density matrix in quantum mechanics of the early universe. It is assumed that the latter represents quantum mechanics with fundamental length. It is demonstrated that the obtained results agree well with the canonical viewpoint that in the processes involving black holes pure states go to the mixed ones in the assumption that all measurements are performed by the observer in a well-known quantum mechanics. Also it is shown that high entropy for Planck remnants of black holes appearing in the assumption of the Generalized Uncertainty Relations may be explained within the scope of the density matrix entropy introduced by the author previously. It is noted that the suggested paradigm is consistent with the Holographic Principle. Because of this, a conjecture is made about the possibility for obtaining the Generalized Uncertainty Relations from the covariant entropy bound at high energies in the same way as R. Bousso has derived Heisenberg uncertainty principle for the flat space.

gr-qc↗
arXiv2004

Some Implications of the Density Matrix Deformation in Statistical Mechanics of the Early Universe

This work is an extension of the study into statistical mechanics of the early Universe that has been the subject in prior works of the author, the principal approach being the density matrix deformation. In the work it is demonstrated that the previously derived exponential ansatz may be successfully applied to the derivation of the free and average energy deformation as well as entropy deformation. Based on the exponential ansatz, the derivation of a statistical-mechanical Liouville equation as a deformation of the quantum-mechanical counterpart is presented. It is shown that deformed Liouville equation will possess nontrivial components as compared to the normal equation in two cases: for the original singularity (i.e. early Universe) and for black hole, that is in complete agreement with the results obtained by the author with coworkers in earlier works devoted to the deformation in quantum mechanics at Planck scale. In conclusion some possible applications of the proposed methods are given, specifically for investigation into thermodynamics of black holes.

gr-qc↗
arXiv2003

The Universe as a Nonuniform Lattice in Finite-Volume Hypercube. I.Fundamental Definitions and Particular Features

In this paper a new small parameter associated with the density matrix deformation (density pro-matrix)studied in previous works of the author is introduced into the Generalized Quantum Mechanics (GQM), i.e. quantum mechanics involving description of the Early Universe. It is noted that this parameter has its counterpart in the generalized statistical mechanics. Both parameters offer a number of merits: they are dimensionless, varying over the interval from 0 to 1/4 and assuming in this interval a discreet series of values. Besides, their definitions contain all the fundamental constants. These parameters are very small for the conventional scales and temperatures, e.g. the value of the first parameter is on the order of $\approx 10^{-66+2n}$, where $10^{-n}$ is the measuring scale and the Planck scale $\sim 10^{-33}cm$ is assumed. The second one is also too small. It is demonstrated that relative to the first of these parameters the Universe may be considered as a nonuniform lattice in the four-dimensional hypercube with dimensionless finite-length (1/4)edges. And the time variable is also described by one of the above-mentioned dimensions due to the second parameter and generalized uncertainty relations in thermodynamics. In this context the lattice is understood as a deformation rather than approximation.

hep-th↗