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A. Yu. Zakharov

Publications and source records attributed to A. Yu. Zakharov.

At least 19 recordsLinked to original sources
arXiv2026

Principles of relativistic quantum statistical thermodynamics: a class of exactly solvable models

A system of interacting atoms is represented as an union of two subsystems, one of which is the system of atoms, and the other is an auxiliary scalar covariant field, which is equivalent to a given static interatomic potential of general form only in the non-relativistic approximation. It is shown that the auxiliary field is a superposition of Klein-Gordon fields, the parameters of which are related to singular points of the Fourier transform of the corresponding interatomic potential. The general form of the relativistic Hamiltonian system of interacting atoms is established. It is shown that the exact calculation of the relativistic partition function of a system of interacting atoms, taking into account the field degrees of freedom, reduces to renormalizing the parameters of the auxiliary field. It is established that the field degrees of freedom lead to a divergence in the total energy of a classical relativistic system - an analogue of the ultraviolet catastrophe. Quantization of the auxiliary field eliminates this divergence. The existence of a phase transition within the framework of relativistic quantum statistical thermodynamics has been proven.

quant-ph↗
arXiv2024

On the microscopic foundation of thermodynamics and kinetics. Current status and prospects

A comparative analysis of two concepts aimed at microscopic substantiation of thermodynamics and kinetics has been performed. The first concept is based on the idea of microscopic reversibility of the dynamics of a system of particles, while macroscopic irreversibility is of statistical origin. The second concept is based on the idea of the initial microscopic irreversibility of dynamics, one of the mechanisms of which is the relativistic retardation of interactions between particles.

cond-mat.stat-mech↗
arXiv2022

Field representation of interatomic interactions: from relativistic dynamics to microscopic thermodynamics of both many-body and few-body systems

It is proved that the class of stable interatomic potentials admits an exact representation in the form of a finite or infinite superposition of Yukawa potentials. An auxiliary scalar field is introduced to describe the dynamics of a system of neutral particles (atoms) in the framework of classical field theory. In the case of atoms at rest, this field is equivalent to the interatomic potential, but in the dynamic case it describes the dynamics of a system of atoms interacting through a relativistic classical field. A relativistic Lagrangian for a system consisting of atoms and an auxiliary composite field through which the atoms interact is proposed. Equations are derived for the relativistic dynamics of a system consisting of atoms and an auxiliary field via which the atoms interact. A closed system of equations for the relativistic dynamics of a system consisting of atoms and an auxiliary field through which the atoms interact is derived. In the resulting system, an exact analytical exclusion of field variables is performed, and a closed kinetic equation is derived with respect to the probability-free microscopic atomic distribution function. Keywords: Classical relativistic dynamics; Causality principle; Stable interatomic interactions; Irreversibility phenomenon; Retarded interactions

cond-mat.stat-mech↗
arXiv2021

Relativistic kinetic theory: toward the microscopic substantiation of zeroth law of thermodynamics

An exact closed relativistic kinetic equation is derived for a system of identical classical particles interacting with each other through a scalar field. The microscopic deterministic mechanism of the irreversible equilibration process in a relativistic classical system of interacting particles has been established. Keywords: Irreversible equilibration process; Classical relativistic dynamics; Retarded interactions.

cond-mat.stat-mech↗
arXiv2021

Towards the microscopic foundation of the zeroth law of thermodynamics

The dynamics of free vibrations of a chain of atoms is investigated taking into account the retardation of interactions. It is shown that all oscillations of the circuit are damped. The dynamics of forced vibrations of this chain of atoms is investigated. It is shown that, regardless of the initial conditions, the system passes into a stationary state of dynamic equilibrium with an external field, which depends both on the properties of the system and on the parameters of the external field. A non-statistical dynamic mechanism of the process of irreversible establishment of the state of thermodynamic equilibrium in both many-body and few-body systems is proposed.

cond-mat.stat-mech↗
arXiv2020

Relativism versus statistics in the microscopic foundation of thermodynamics

Highlights: \begin{itemize} \item Relativistic effect of crystal dynamics "freezing". \item Non-statistical model of thermodynamic equilibration. \end{itemize} The dynamics of oscillations of a one-dimensional atomic chain is investigated in the harmonic approximation, taking into account the relativistic effect of retardation of interactions. It is shown that all oscillations of the chain are damped. A non-statistical mechanism for the irreversible thermodynamic equilibration in many-body systems is proposed.

cond-mat.mtrl-sci↗
arXiv2020

Relativistic kinetic theory of classical systems of charged particles: towards the microscopic foundation of thermodynamics and kinetics

In the complete system of equations of evolution of the classical system of charges and the electromagnetic field generated by them, the field variables are excluded. An exact closed relativistic non-Hamiltonian system of nonlocal kinetic equations, that describes the evolution of a system of charges in terms of their microscopic distribution functions, is obtained . The solutions of this system of equations are non-invariant with respect to time reversal, and also have the property of hereditarity.

cond-mat.stat-mech↗
arXiv2018

On physical principles and mathematical mechanisms of the phenomenon of irreversibility

It is shown that the phenomenon of irreversibility in many-body and few-body systems can be explained and described within the framework of the concept of direct (not instantaneous) interaction of particles without using probabilistic hypotheses. The exact solution of the model of a two-particle classical oscillator with retarded interaction between particles is presented. It is established that the interactions retardation leads to appearance of an infinite spectrum of both stationary and non-stationary oscillations, and to non-invariance of the solution with respect to time reversal as well.

cond-mat.stat-mech↗
arXiv2017

Irreversibility in two-body system. Toy model

It is shown that the irreversible behavior of classical systems of interacting particles is a common property for both few-body and many-body systems. It is due to the delay in the interactions between the particles. PACS: 45.50.Jf Few- and many-body systems; 82.40.Bj Oscillations, chaos, and bifurcations; 05.70.-a Thermodynamics. Keywords: irreversibility, interactions retardation.

cond-mat.stat-mech↗
arXiv2017

Low- and high-temperature anomalies in the physical properties of solid methane

Near 20.48K and in the temperature range 60--70K, anomalous behavior of thermodynamic, spectral, plastic, elastic and other properties of solid methane is observed. The anomalies in the vicinity of 20.48K are due to the phase $α-β$ transition. Anomalies in a relatively wide range of 60--70K are shown to be related to the essentially quantum nature of the collective rotation of methane molecules. The provided analysis of the high-temperature anomalies encompasses a more extensive set of phenomena in comparison with the low-temperature ones. Key words: solid methane, anomalies of physical properties, phase transition, rotational temperature, quantum-classical transition.

cond-mat.mtrl-sci↗
arXiv2017

On the status of the Born-Oppenheimer expansion in molecular systems theory

It is shown that the adiabatic Born-Oppenheimer expansion does not satisfy the necessary condition for the applicability of perturbation theory. A simple example of an exact solution of a problem that can not be obtained from the Born-Oppenheimer expansion is given. A new version of perturbation theory for molecular systems is proposed.

cond-mat.stat-mech↗
arXiv2016

Low-frequency internal friction (LFIF) as express-method for identification of cryocrystals in pores of the solids

We show that studying of low-frequency internal friction (LFIF) of solid samples at low temperatures allows determining the presence of various gases absorbed, for some reasons, in pores and caverns of the solids. The gases come over to a solid state (cryocrystals) and exist in the pores under corresponding thermodynamic conditions giving an additional contribution to the LFIF spectra. The spectra reflect the special points of the gases (temperatures of melting or phase transitions). This information gives a real opportunity for identification of gas in the matrix, i.e. the studied solids. This may be of great importance for investigations of cosmic or geological samples, for instance, asteroids, meteorites, rock formations, etc. The LFIF method allows identification of gas media surrounding the studied sample.

cond-mat.mtrl-sci↗
arXiv2014

Exact equation for classical many-particle systems in closed form: from mechanics to statistical thermodynamics

The exact equations of motion for microscopic density of classical particles number with account of inter-particle interactions and external field in closed form are derived. An integral equation for equilibrium distributions of the particles is deduced. No statistical or probabilistic hypotheses and assumption in these deductions have been used. Some well known results of equilibrium statistical mechanics are deduced from the obtained equations as simple limiting cases. The wave equation for almost homogeneous systems with inter-particle interactions are obtained. Connection between inter-particle potential and dispersion law of sound is established. Keywords: Many-body systems dynamics; inter-atomic potentials; phase equilibrium PACS 05.20.-y; 05.10.-a; 05.70.Ln

cond-mat.stat-mech↗
arXiv2014

Modeling of hysteresis phenomena in crystalline ferroelectrics: hysteresis loops shape control by means of electric field parameters

Description of domains switching processes in crystalline ferroelectrics by means of relaxation type equations with account of variable external electric field is proposed. Exact solution of these equations in closed analytical form at arbitrary dependence of electric field on time is obtained. A connection between frequency of sinusoidal external field and hysteresis loops shapes is analysed by numerical way. The calculation results are in qualitative accordance with experimental data. PACS: 77.80.Fm, 77.80.Dj, 77.80.-e Keywords: ferroelectrics, switching process, hysteresis, polarization

cond-mat.mtrl-sci↗
arXiv2014

Abnormal behavior of crystalline methane in temperature interval $60-70~K$. From experiment to theory

The paper presents an analysis of mechanical, structural, thermophysical and spectral properties of solid methane in temperature interval $0.5T_{tr} -T_{tr}$ ($T_{tr}$ is the triple point temperature) under equilibrium vapor pressure. It is shown that the anomalies of the studied properties at temperatures 60--70~K have been observed in the body of the reviewed papers. A concept of "topons" (collective excitations of rotational degrees of freedom in solid methane) is proposed. A whole of the observed anomalies can be explained in the frames of this concept. Key words: solid methane, quantum crystals, rotational degrees of freedom, thermophysical and mechanical properties of the crystals

cond-mat.mtrl-sci↗