arXiv subjects

Yu. M. Poluektov

Publications and source records attributed to Yu. M. Poluektov.

36 records · Page 2Linked to original sources

arXiv2020

Accounting for the long-range forces in the model of hard sphere

A method for taking into account the long-range potential of atoms in the framework of the hard-sphere model is proposed. It is shown that thermodynamic quantities can be represented as a sum of three contribution: that of an ideal gas, the interaction of hard sphere, and the long-range potential. In the leading approximation on density, the corrections to the virial coefficient and heat capacity due to the smooth component of the potential are calculated. Attention is drawn to the fact that the effects determined by the long-range part of of the potential can be described in the framework of the self-consistent field model.

cond-mat.stat-mech↗

arXiv2020

The two-parameter Debye model

When analyzing thermodynamic and kinetic properties of crystals whose anisotropy is not large and the considered effects do not relate to the existence of singled-out directions in crystals, one may use a more simple model of an isotropic medium with a good accuracy, after having chosen its parameters in an optimal way. Based on the quantum mechanical description it is shown that the method of approximation of the moduli of elasticity of a crystal by the model of an isotropic medium, proposed earlier in [2], follows from the requirement of the minimal difference between the free energies of a crystal and an approximating isotropic medium. The two-parametric Debye model is formulated, which, in contrast to the standard model where the average speed of phonons is introduced, takes into account the existence in an isotropic medium of both longitudinal and transverse phonons. The proposed model contains, except the Debye energy, an additional dimensionless parameter and, consequently, the law of corresponding states for the heat capacity being characteristic of the standard model does not hold. With taking account of the two phonon branches the structure of the density of phonon states proves to be more complex as compared to the standard model and has a singularity that resembles Van Hove singularities in real crystals. As an example, an application of the two-parametric Debye theory to such crystals of the cubic system as tungsten, copper, lead is considered. It is shown that the calculation of the low-temperature heat capacity of these crystals by means of the approximated moduli of elasticity within the framework of the two-parametric model leads to a considerably better agreement with experiment than in the case of the standard Debye model.

cond-mat.stat-mech↗

arXiv2019

Waves in a Bose-Einstein condensate of atoms with a dipole moment

Based on the modified Gross-Pitaevskii equation for atoms with intrinsic dipole moments which accounts for the relaxation of a condensate, the dipole-dipole interaction and the interaction of atoms with the electromagnetic field, the propagation of the sound and electromagnetic waves in a Bose-Einstein condensate is studied. Owing to hybridization of the electromagnetic and sound waves near the resonance frequency of an atom, there arise the two branches of excitations in which the electromagnetic oscillations transform into the sound oscillations and vice versa. It is shown that under hybridization the crucial role is played by the dipole-dipole interaction, which leads to a substantial increase of the repulsion between the branches of the spectrum. The influence of the dissipative effects connected with the relaxation of the macroscopic wave function of the condensate and the imaginary part of the polarizability of an atom on the form of the dispersion curves is investigated.

cond-mat.quant-gas↗

arXiv2019

Nonlinear effects in the phonon system of diamond crystal

Thermodynamic properties of diamond are theoretically investigated on the ground of self-consistent description of a phonon gas in lattice, which generalizes the Debye model with taking into account the phonon-phonon interaction. It is shown that, at high temperatures, the theory predicts the linear in the temperature deviation of the isochoric heat capacity from the Dulong-Petit law. Unlike for the most crystals, where the decrease in the isochoric heat capacity is observed, our calculations for diamond predict the linear increase of the isochoric heat capacity with the temperature, viewed experimentally. The isobaric heat capacity of diamond, similar to other substances, linearly increases with the temperature.

cond-mat.mtrl-sci↗

arXiv2018

On the dependence of the speed of light in vacuum on temperature

It is shown that the interaction of the electromagnetic field with the vacuum of the electron-positron field gives rise to dependence of the speed of light propagation on the radiation temperature. Estimation show that in the modern epoch, even at very high temperatures, such for example which exist in the star interiors, the temperature-dependent correction to the speed of light proves to be extremtly small. But in the cosmological model of the hot Universe, in the first instances after the Big Bang the temperature was so high that the speed of light exceeded its present value by many orders of magnitude. The effect of dependence of the speed of light on temperature must be important for understanding the early evolution of the Universe.

physics.gen-ph↗

arXiv2017

Bose-Einstein condensation in a mixture of interacting Bose and Fermi particles

A self-consistent field model for a mixture of Bose and Fermi particles is formulated. There is explored in detail the case of a delta-like interaction, for which the thermodynamic functions are obtained, and Bose-Einstein condensation of interacting particles in the presence of the admixture of fermions is studied. It is shown that the admixture of Fermi particles leads to reducing of the temperature of Bose-Einstein condensation and smoothing of features of thermodynamic quantities at the transition temperature. As in the case of a pure Bose system, in the state of a mixture with condensate the dependence of the thermodynamic potential on the interaction constant between Bose particles has a nonanalytic character, so that it proves impossible to develop the perturbation theory in the magnitude of interaction of Bose particles.

cond-mat.quant-gas↗

arXiv2017

Thermodynamics of the Fermi gas in a nanotube

For the ideal Fermi gas that fills the space inside a cylindrical tube, there are calculated the thermodynamic characteristics in general form for arbitrary temperatures, namely: the thermodynamic potential, energy, entropy, equations of state, heat capacities and compressibilities. All these quantities are expressed through the introduced standard functions and their derivatives. The radius of the tube is considered as an additional thermodynamic variable. It is shown that at low temperatures in the quasi-one-dimensional case the temperature dependencies of the entropy and heat capacities remain linear. The dependencies of the entropy and heat capacities on the chemical potential have sharp maximums at the points where the filling of a new discrete level begins. The character of dependencies of thermodynamic quantities on the tube radius proves to be qualitatively different in the cases of fixed linear and fixed total density. At the fixed linear density these dependencies are monotonous and at the fixed total density they have an oscillating character. Key words: Fermi particle, nanotube, thermodynamic functions, low-dimensional systems, equation of state, heat capacity, compressibility

physics.gen-ph↗

arXiv2016

Thermodynamics of the Fermi gas in a quantum well

For the ideal Fermi gas that fills a quantum well confined by two parallel planes, there are calculated the thermodynamic characteristics in general form for arbitrary temperatures, namely: the thermodynamic potential, energy, entropy, equations of state, heat capacities and compressibilities. The distance between planes is considered as an additional thermodynamic variable. Owing to the anisotropy, the pressure of the Fermi gas along and transverse to the planes is different, so that the system is characterized by two equations of state and a set of different heat capacities. Limiting cases of low and high temperatures are considered. The temperature dependencies of the entropy and heat capacities at low temperatures remain linear, just as in the volume case, and their dependencies on the chemical potential and density undergo jumps at the beginning of the filling of new discrete levels. It is shown that the behavior of thermodynamic quantities with the distance between plates can be either oscillating or monotonic, depending on what quantity is assumed to be fixed: the volume or surface density. For high temperatures the corrections to thermodynamic quantities are obtained, which are proportional to the ratio of the thermal de Broglie wavelength to the distance between planes.

cond-mat.stat-mech↗

arXiv2016

Modified perturbation theory for the Yukawa model

A new formulation of perturbation theory for a description of the Dirac and scalar fields (the Yukawa model) is suggested. As the main approximation the self-consistent field model is chosen, which allows in a certain degree to account for the effects caused by the interaction of fields. Such choice of the main approximation leads to a normally ordered form of the interaction Hamiltonian. Generation of the fermion mass due to the interaction with exchange of the scalar boson is investigated. It is demonstrated that, for zero bare mass, the fermion can acquire mass only if the coupling constant exceeds the critical value determined by the boson mass. In this connection, the problem of the neutrino mass is discussed.

physics.gen-ph↗

arXiv2016

A simple model of Bose-Einstein condensation of interacting particles

A simple model of Bose-Einstein condensation of interacting particles is proposed. It is shown that in the condensate state the dependence of thermodynamic quantities on the interaction constant does not allow an expansion in powers of the coupling constant. Therefore it is impossible to pass to the Einstein model of condensation in an ideal Bose gas by means of a limiting passage, setting the interaction constant to zero. The account for the interaction between particles eliminates difficulties in the description of condensation available in the model of an ideal gas, which are connected with fulfillment of thermodynamic relations and an infinite value of the particle number fluctuation in the condensate phase.

cond-mat.stat-mech↗

arXiv2015

The self-consistent field model for Fermi systems with account of three-body interactions

On the basis of a microscopic model of self-consistent field, the thermodynamics of the many-particle Fermi system at finite temperatures with account of three-body interactions is built and the quasiparticle equations of motion are obtained. It is shown that the delta-like three-body interaction gives no contribution into the self-consistent field, and the description of three-body forces requires their nonlocality to be taken into account. The spatially uniform system is considered in detail, and on the basis of the developed microscopic approach general formulas are derived for the fermion's effective mass and the system's equation of state with account of contribution from three-body forces. The effective mass and pressure are numerically calculated for the potential of "semi-transparent sphere" type at zero temperature. Expansions of the effective mass and pressure in powers of density are obtained. It is shown that, with account of only pair forces, the interaction of repulsive character reduces the quasiparticle effective mass relative to the mass of a free particle, and the attractive interaction raises the effective mass. The question of thermodynamic stability of the Fermi system is considered and the three-body repulsive interaction is shown to extend the region of stability of the system with the interparticle pair attraction. The quasiparticle energy spectrum is calculated with account of three-body forces.

cond-mat.stat-mech↗

arXiv2015

The equation of state and the quasiparticle mass in the degenerate Fermi system with an effective interaction

General formulas are derived for the quasiparticle effective mass and the equation of state of the Fermi system with account of the interparticle attraction at long distances and repulsion at short distances. Calculations are carried out of the equation of state and the effective mass of the Fermi system at zero temperature with the use of the modified Morse potential. It is shown that the pair repulsive forces promote a decrease of the effective mass, and the attractive forces promote its increase. With a certain choice of the parameters of the potential the dependence of the pressure on the density has a nonmonotonic character, which enables to describe the coexistence of the liquid and gaseous phases. The influence of three-body interactions on the equation of state and the effective mass is considered. The calculation results are compared with experimental data concerning the quasiparticle effective mass in the liquid $^3$He. Key words: normal Fermi liquid, effective mass, quasiparticle, equation of state, interaction potential

cond-mat.stat-mech↗

arXiv2014

Critical temperature of the superfluid transition in Fermi-system at an arbitrary pair potential

A method for calculation of the critical temperature of transition of a many-particle Fermi system into a superfluid or a superconducting state at an arbitrary pair potential of the interparticle interaction is proposed. An original homogeneous integral equation, that determines the critical temperature, is transformed into a homogeneous integral equation with a symmetric kernel that enables application of a general theory of integral equations for calculation. Examples are given of calculation of the superconducting transition critical temperature for the BCS potential with the Coulomb repulsion and the critical temperature of the superfluid transition of liquid helium-3 into $p$-wave pairing state for the Morse potential.

cond-mat.stat-mech↗

arXiv2014

Propagation of electromagnetic waves in Bose-Einstein condensate of atoms with dipole moments

We study the propagation of electromagnetic waves in the Bose-Einstein condensate of atoms with both intrinsic dipole moments and those induced by the electric field. The modified Gross--Pitaevskii equation is used, which takes into account relaxation and interaction with the electromagnetic field. Two cases are considered: 1) when the dispersion curves of the electromagnetic wave and of the condensate excitations do not intercross and 2) when the condensate excitations' spectrum has a gap and the two dispersion curves do intercross. In the second case the two branches hybridize. It is shown that propagation of sound waves can be accompanied by oscillation of the electromagnetic field. The impact is studied of the dipole-dipole interaction on the character of electromagnetic and acoustic waves' propagation in the Bose-Einstein condensate.

cond-mat.quant-gas↗

arXiv2013

On the quantum-field description of many-particle Bose systems with spontaneously broken symmetry

A quantum-field approach to studying the Bose systems at finite temperatures and in states with spontaneously broken symmetry, in particular in a superfluid state, is proposed. A generalized model of a self-consistent field (SCF) for spatially inhomogeneous many-particle Bose systems is used as the initial approximation. A perturbation theory has been developed, and a diagram technique for temperature Green's functions (GFs) has been constructed. The Dyson's equations joining the eigenenergy and vertex functions have been deduced.

cond-mat.stat-mech↗

arXiv2013

Role of single-particle and pair condensates in Bose systems with arbitrary intensity of interaction

We study a superfluid Bose system with single-particle and pair condensates on the basis of a half-phenomenological theory of a Bose liquid not involving the weakness of interparticle interaction. The coupled equations describing the equilibrium state of such system are derived from the variational principle for entropy. These equations are analyzed at zero temperature both analytically and numerically. It is shown that the fraction of particles in the single-particle and pair condensates essentially depends on the total density of the system. At densities attainable in condensates of alkali-metal atoms, almost all particles are in the single-particle condensate. The pair condensate fraction grows with an increasing total density and becomes dominant. It is shown that at density of liquid helium, the single-particle condensate fraction is less than 10%, which agrees with experimental data on inelastic neutron scattering, Monte Carlo calculations and other theoretical predictions. The ground state energy, pressure, and compressibility are found for the system under consideration. The spectrum of single-particle excitations is also analyzed.

cond-mat.stat-mech↗

arXiv2013

On the quantum-field description of many-particle Fermi systems with spontaneously broken symmetry

A quantum-field approach for describing many-particle Fermi systems at finite temperatures and with spontaneously broken symmetry has been proposed. A generalized model of self-consistent field (SCF), which allows one to describe the states eligible for this system with various symmetries, is used as the initial approximation. A perturbation theory has been developed, and a diagram technique for temperature Green's functions (GFs) has been constructed. The Dyson's equation for the self-energy and vertex parts has been deduced.

cond-mat.stat-mech↗

arXiv2010

Short-Wave Excitations in Non-Local Gross-Pitaevskii Model

It is shown, that a non-local form of the Gross-Pitaevskii equation allows to describe not only the long-wave excitations, but also the short-wave ones in the systems with Bose-condensate. At given parameter values, the excitation spectrum mimics the Landau spectrum of quasi-particle excitations in superfluid Helium with roton minimum. The excitation wavelength, at which the roton minimum exists, is close to the inter-particle interaction range. It is shown, that the existence domain of the spectrum with a roton minimum is reduced, if one accounts for an inter-particle attraction.

cond-mat.stat-mech↗