Yu. A. Tserkovnikov

Correlation functions of a Heisenberg ferromagnet in the paramagnetic region

ConclusionsIn the present paper, in the framework of the coupled-mode approximation for the second-order equations (2.6)–(2.9) we have obtained an approximate closed system of equations (2.10)–(2.14) for the spin correlation functions of a Heisenberg ferromagnet in a vanishing external magnetic field and at temperatures θ above the critical temperature (θ≥θc)., In principle, Eqs. (2.10)–(2.14) make it possible to investigate the behavior of the correlation functions in the entire investigated temperature range, including the critical point. Equations (2.10)–(2.14) are very complicated, and a numerical calculation is needed to analyze them.In the fourth section, we obtained interpolation formulas that make it possible to describe in some detail the behavior of the spectral density at both high and low frequencies. It would be expedient to find first the solution, of the simplified system of equations obtained from (2.10)–(2.14) by replacement of the Greens function (2.10) and the spectral density (3.2) by their interpolation expressions (4.2) and (4.3). Substituting (4.3) in (3.3) and (3.4), we obtain equations for λ and Δ, in terms of which all the remaining quantities can be expressed. The solution obtained from the simplified system can be used further as initial approximation in the solution of the system of equations (2.10)–(2.14). However, this problem goes beyond the framework of the given paper.

Two-Time Temperature Green's Functions in Kinetic Theory and Molecular Hydrodynamics: III. Taking the Interaction of Hydrodynamic Fluctuations into Account

We describe a systematic method for constructing equations for Greens functions in molecular hydrodynamics and kinetics problems. The method allows consecutively accounting for the contribution to the generalized kinetic coefficients due to the interaction of two, three, and more hydrodynamic modes. In contrast to the standard perturbation theory in the coupling constant, the consecutive approximations are taken with respect to the degree of higher correlations described by irreducible functions.

Two-time temperature Green's functions in kinetic theory and molecular hydrodynamics: I. The chain of equations for the irreducible functions

We develop a scheme for constructing chains of equations for the irreducible Greens functions. The structure of the equations allows going beyond the usual perturbation theory in solving specific problems. We obtain general relations that allow any correlation function to be expressed through solutions of an infinite chain of equations for the irreducible functions.

Molecular hydrodynamics of degenerate weakly nonideal bose gas. I. Generalized equations of two-fluid hydrodynamics

A degenerate weakly nonideal Bose gas is investigated at temperatures near zero. Relations connecting the irreducible Greens functions are used to obtain exact expressions for the two-time temperature-dependent Greens functions. In the case of weak nonideality an expression possessing interpolation properties with respect to the frequency and momentum is obtained for the density—density Greens function. At low frequencies, the results of two-fluid hydrodynamics are reproduced. At wavelengths less than the mean free path the energy of the elementary excitations and the damping obtained in the paper agree with the results of perturbation theory with respect to the coupling constant. An expression for the operator of the superfluid velocity is obtained.

Molecular hydrodynamics of a weakly degenerate nonideal bose-gas II. Green functions and kinetic coefficients

The nonideal degenerate Bose-system at a temperature close to zero is investigated by N. N. Bogolyubov and D. N. Zubarevs method of collective variables. Applicable to a wide range of frequencies and wave vectors, interpolated expressions for the Green functions of the densities of conserved quantities and for the superfluid velocity potential are derived from exact relations. The criteria defining the validity domain of the hydrodynamic approximation are obtained. The kinetic coefficients of two-liquid hydrodynamics at temperatures close to zero are calculated for a weakly nonideal Bose-gas. A comparison with the method employing the kinetic equation for quasi-particles is made.

Kinetic equations in the method of two-time finite-temperature Green's functions. I. Renormalization of the collision integral

A system of equations that includes a generalized kinetic equation and equations for the static correlation functions is constructed for a normal quantum system of interacting Bose and Fermi particles with two-body interaction on the basis of the method of two-time finite-temperature Greens functions. The equations are in general valid for systems with arbitrary density of the particles. A method of successive approximation that makes it possible to go beyond the usual low-density expansion is discussed. The proposed method leads to a renormalization of the collision integral and makes it possible to obtain correlation functions for the total energy density, including its potential part.

The method of two-time Green's functions in the molecular hydrodynamics of a superfluid

For a system of interacting bosons at temperature below the critical temperature the single-particle functions as well as the Greens functions for the fluctuations of the density and the temperature are constructed on the basis of the hierarchy of equations for the irreducible Greens functions. In the limiting case of low frequency and small wave vectors a comparison is made with the results obtained on the basis of the two-fluid hydrodynamics of a superfluid Bose liquid. It is shown that the macroscopic parameters of the two-fluid hydrodynamics (the susceptibilities and the transport coefficients) are completely determined in the framework of the microscopic approach.