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Отримано нове немарковське рівняння дифузії частинок у просторово неоднорідному середовищі з фрактальною структурою та узагальнене рівняння дифузії Кеттано–Максвелла з урахуванням просторово-часової нелокальності. Знайдено дисперсійні співвідношення для рівняння дифузії типу Кеттано–Максвелла з урахуванням просторово-часової нелокальності у дробових похідних. Розраховано частотний спектр, фазову та групову швидкості й показано його хвильову поведінку зі стрибкоподібними розривами, які проявляються також у зміні фазової швидкості. The new non-Markovian diffusion equations of ions in spatially heterogeneous environment with fractal structure and generalized Cattaneo–Maxwell diffusion equation with taking into account the space-time nonlocality are obtained. Dispersion relations for the Cattaneo–Maxwell-type diffusion equation with taking into account the space-time nonlocality in fractional derivatives are found. The frequency spectrum, phase and group velocities are calculated. It is shown that it has a wave behavior with discontinuities, which are also manifested in behavior of the phase velocity.

Based on the non-Markov diffusion equation taking into account the spatial fractality and modeling for the generalized coefficient of particle diffusion $D^{\alpha\alpha'}(\mathbf{r},\mathbf{r}';t,t')=W(t,t')\bar{D}^{\alpha\alpha'}(\mathbf{r},\mathbf{r}')$ using fractional calculus the generalized Cattaneo--Maxwell--type diffusion equation in fractional time and space derivatives has been obtained. In the case of a constant diffusion coefficient, analytical and numerical studies of the frequency spectrum for the Cattaneo--Maxwell diffusion equation in fractional time and space derivatives have been performed. Numerical calculations of the phase and group velocities with change of values of characteristic relaxation time, diffusion coefficient and indexes of temporal $\xi$ and spatial $\alpha$ fractality have been carried out., Comment: 23 pages, 4 figures

We presented a general approach for obtaining the generalized transport equations with fractional derivatives by using the Liouville equation with fractional derivatives for a system of classical particles and Zubarev’s nonequilibrium statistical operator (NSO) method within Renyi statistics. New non-Markovian diffusion equations for particles in spatially heterogeneous environment with fractal structure and a generalized Cattaneo-type diffusion equation with taking into account nonlocality of space–time are obtained. Different models of frequency-dependent memory functions, which lead to known diffusion equations with nonlocality of space–time and their generalizations are studied.

A formulation of nonequilibrium thermo-field dynamics has been performed using the nonequilibrium statistical operator method by D.N. Zubarev. Generalized transfer equations for a consistent description of the kinetics and hydrodynamics of the dense quantum field system with strongly-bound states are derived.

In the present paper we used ion-polarization model to study collective excitations in ionic melts. Based on the extended model for collective dynamics in ionic melts (which takes into account fluctuations of charge density, charge current, and its time derivative) we obtained the set of collective excitations in the system, containing relaxation mode related to electric conductivity, two propagating optic-like modes and relaxation mode due to polarization processes. The received analytical expressions for the collective modes take into account corrections caused by ion polarizability comparing to rigid-ion model. The obtained results correctly describe a reduction of frequency of optic-like modes and an increase of damping due to polarization processes. The results are consistent with other theoretical works and results of computer simulations.

The new non-Markovian electrodiffusion equations of ions in spatially heterogeneous environment with fractal structure and generalized Cattaneo-type diffusion equation with taking into account fractality of space-time are obtained. Different models of the frequency dependence of memory functions, which lead to known diffusion equations with fractality of space-time and their generalizations are considered. Отримано новi немарковськi рiвняння електродифузiї iонiв у просторово неоднорiдному середовищi з фрактальною структурою та узагальненi рiвняння дифузiї типу Кеттано з врахуванням просторово-часової фрактальностi. Розглянуто рiзнi моделi частотної залежностi для функцiй пам’ятi, якi приводять до вiдомих рiвнянь дифузiї з просторово-часовою фрактальнiстю, а також їх узагальнень.

We discuss the important role of the Zubarev nonequilibrium statistical operator method in the generalized molecular hydrodynamics of fluids. Using this method allows developing a consistent approach of generalized collective excitations for simple, ion, polar, magnetic, and some other fluids. We construct a nonequilibrium statistical operator and derive the corresponding transport equations for a system that relaxes and passes into the state of molecular hydrodynamics.

Chain of kinetic equations for non-equilibrium single, double and s-particle distribution functions of particles is obtained taking into account nonlin- ear hydrodynamic fluctuations. Non-equilibrium distribution function of non-linear hydrodynamic fluctuations satisfies a generalized Fokker-Planck equation. The method of non-equilibrium statistical operator by Zubarev is applied. A way of calculating of the structural distribution function of hydrodynamic collective variables and their hydrodynamic velocities (above Gaussian approximation) contained in the generalized Fokker-Planck equa- tion for the non-equilibrium distribution function of hydrodynamic collective variables is proposed., 31 pages

Generalized transport equations for description of diffusion-reaction processes in chemically active mixtures are obtained. The nonequilibrium statistical operator method by Zubarev is used and both strong and weak nonequilibrium processes are analyzed. In the approximation of the second order in fluctuations we get generalized equations of chemical kinetics for bimolecular reactions with generalized rate constants. In the case of spatial uniformity the integro-differential equation for the matrix of partial scattering functions is received, which are related to partial dynamic structure factors of chemically reactive system by the time Fourier transformation.

Dynamic properties of multicomponent mixtures of magnetic and non-magnetic particles were considered. We start from the general case of a multicomponent mixture, some components of which possess a magnetic momentum, being described by m + 2 parameters of abbreviated description. The equations of generalized hydrodynamics and those for time correlation functions are derived. Then we calculate eigenvalues of the hydrodynamic equations for small wave-number k , which yielded sound velocity and sound damping coefficients for two propagating modes, and damping coefficients for the rest modes which are purely diffusive. The scheme, which allows us to obtain weight coefficients for time correlation functions is proposed. Expressions for time correlation functions are analyzed for the paramagnetic case, when the coupling between the spin and fluid degrees of freedom can be neglected.

The collective excitation spectrum of semiquantum 4 He at temperatures T = 4 K and 8 K is investigated on the basis of a thermoviscous model of a fluid. Partial contributions of every collective mode to the symmetrized dynamic structure factor are evaluated. The problem is considered in relation with neutron scattering experimental data and theoretical results previously known.

The dynamic properties of semiquantum 4He are analyzed at two temperatures above the point of superfluid phase transition. Investigations are carried out in the framework of the dynamic thermal viscous model for low and intermediate values of the wave vector. The “momentum–momentum” and “enthalpy–enthalpy” time correlation functions are evaluated and the partial contributions of the collective excitations to these functions are separated. The recurrent relations for memory kernels are used to calculate the time–space dispersion of the generalized transport coefficients.

An Enskog-Landau kinetic equation for a many-component system of charged hard spheres is proposed. It has been obtained from the Liouville equation with modified boundary conditions by the method of nonequilibrium statistical operator. On the basis of this equation the normal solutions and transport coefficients such as bulk kappa and shear eta viscosities, thermal conductivity lambda, mutual diffusion D^{\alpha\beta} and thermal diffusion D_T^\alpha have been obtained for a binary mixture in the first approximation using the Chapman-Enskog method. Numerical calculations of all transport coefficients for mixtures Ar-Kr, Ar-Xe, Kr-Xe with different concentrations of compounds have been evaluated for the cases of absence and presence of long-range Coulomb interactions. The results are compared with those obtained from other theories and experiment., Comment: 24 LaTeX209 pages, 3 EPS figures (4 files). To be published in Physica A

A general theoretical approach is developed for describing the dynamic properties of semiquantum fluids on the basis of the nonequilibrium statistical operator technique. A set of equations of generalized hydrodynamics is derived and the particular case of thermo-viscoelastic model of a fluid is analyzed in details in the hydrodynamic limit. The case of intermediate and large values of the wave vector is also discussed. The Markov approximation for transport kernels is used to obtain a closed set of equations for dynamic correlation functions. The problem is considered in the context of relation with the experimental data on neutron scattering and the theoretical results known previously in the literature.

The Zubarev nonequilibrium statistical operator is used to describe the generalized hydrodynamic state of a magnetic fluid in an external magnetic field. The magnetic fluid is modeled with “liquid-state” and “magnetic” subsystems described using the classical and quantum statistics methods respectively. Equations of the generalized statistical hydrodynamics for a magnetic fluid in a nonhomogeneous external magnetic field with the Heisenberg spin interaction are derived for “liquid-state” and “magnetic” subsystems characterized by different nonequilibrium temperatures. These equations can be used to describe both the weakly and strongly nonequilibrium states. Some limiting cases are analyzed in which the variables of one of the subsystems can be formally neglected.

The generalized transport equations for a consistent description of kinetic and hydrodynamic processes in dense gases and liquids are considered. The inner structure of the generalized transport kernels for these equations is established. It is shown how in this approach to obtain the transport equation of molecular hydrodynamics. For the model potential of interaction presented as a sum of the hard spheres potential and certain long-range potential a spectrum of collective modes in the system is investigated., 28 pages

Using Zubarev's method of nonequilibrium statistical operator, the generalized hydrodynamic equations are obtained for a model of magnetic liquid in an inhomogeneous external field. In this model the “liquid” subsystem is treated as a classical one and the “magnetic” subsystem is described by quantum mechanical methods. The properties of the transport equations are analysed in the case of a weak nonequilibrium. The equations for time correlation functions and collective mode spectrum are also found in the same manner. It is shown that the generalized hydrodynamic equations reduce to the well-known results in the limiting cases when the dynamic variables of one subsystem are formally neglected. As an illustration, a simple model of spin relaxation is considered, and the frequency matrix and the matrix of memory functions are calculated. A comparison with previous works is made.

Statistical description of hydrodynamic processes for ionic melts is proposed with taking into account polarization effects caused by the deformation of external ionic shells. This description is carried out by means of the Zubarev nonequilibrium statistical operator method, appropriate for investigations of both strong and weak nonequilibrium processes. The nonequilibrium statistical operator and the generalized hydrodynamic equations that take into account polarization processes are received for ionic-polarization model of ionic molten salts when the nonequilibrium averaged values of densities of ions number, their momentum, dipole momentum and total energy are chosen for the reduced description parameters. A spectrum of collective excitations is investigated within the viscoelastic approximation for ion-polarization model of ionic melts., Comment: 24 pages, RevTex4.1-format, no figures

Zubarev's nonequilibrium statistical operator method is used to give a statistical description of a nonequilibrium plasma in its electromagnetic self-field. Generalized transport equations are obtained for the charged particles and the oscillators of the electromagnetic field with allowance made for the local conservation laws. The case of a nonequilibrium plasma is considered.

The problem of relaxation of a nonequilibrium state to the state of molecular hydrodynamics is considered for a classical system of interacting particles using the Zubarev nonequilibrium statistical operator method. The wave-vector and frequency dependencies of the dynamical structure factor and momentum-momentum transverse correlation function are investigated on the basis of the appropriate generalized transport equations. Comparison with the results of molecular hydrodynamics and molecular-dynamics simulations is given and the characteristic time intervals of the studied relaxation processes are determined.

The development of methods of construction of the theory of nonequilibrium processes for finite-temperature quantum-field systems is one of the important directions of modern theoretical physics. The modern methods of quantum field theory [1-8], on the one hand, and nonequilibrium statistical mechanics [9-16] on the other, are powerful tools in investigations of interacting quantum fields and particles. The unification of these methods can be helpful and have significant influence on the solution of many problems in the study of nonequilibrium states of finite-temperature quantum-field systems. In earlier years, the methods of quantum field theory (Green's function method, renormalization-group method) were helpful in statistical mechanics [17-20] (for example, in the theory of magnetism [21], in the theory of phase transitions [22,23]).

In present work a calculation of transfer coefficients for many-component dense gases for charged and non-charged hard spheres is carried out using the Enskog-Landau kinetic equation which takes into account realistic particle sizes., 4 pages, 2 eps-figures

Using charged hard spheres model as an example, the dense one-component plasma is considered. For this model the Enskog-Landau kinetic equation is obtained and its normal solution is found using the Chapman-Enskog method. Transport coefficients are obtained numerically and analytically and compared with the experimental data available., 13 LaTeX209 pages, 4 figures (emline-format for LaTeX)

Nonstationary and nonequilibrium processes are considered on the basis of an Enskog-Landau kinetic equation using a boundary conditions method. A nonstationary solution of this equation is found in the pair collision approximation. This solution takes into account explicitly the influence of long-range interactions. New terms to the transport coefficients are identified. An application of the boundary conditions method to hydrodynamic description of fast processes is discussed., Comment: 11 LaTeX pages using Elsevier format elsart.sty

A consistent statistical description of kinetics and hydrodynamics of dusty plasma is proposed based on the Zubarev nonequilibrium statistical operator method. For the case of partial dynamics the nonequilibrium statistical operator and the generalized transport equations for a consistent description of kinetics of dust particles and hydrodynamics of electrons, ions and neutral atoms are obtained. In the approximation of weakly nonequilibrium process a spectrum of collective excitations of dusty plasma is investigated in the hydrodynamic limit., Comment: 31 pages, no figures

A study is made of the correlation functions of the fluctuations of the mass and charge densities and their fluxes and the generalized transport coefficients for ionic systems as functions of the wave vector kappa and the frequency omega by the nonequilibrium statistical functional method. Numerical calculations are made of the correlation functions of the fluctuations of the mass and charge and their fluxes for ionic molten NaCl.