Quantum transport equations for Bose systems taking into account nonlinear hydrodynamic processes

TL;DR

This paper develops a quantum kinetic framework for Bose systems that incorporates nonlinear hydrodynamic fluctuations, providing equations that describe both kinetic and hydrodynamic processes including turbulence.

Contribution

It introduces a unified approach using the nonequilibrium statistical operator to derive kinetic and generalized Fokker-Planck equations accounting for nonlinear hydrodynamic fluctuations in quantum Bose systems.

Findings

Derived a kinetic equation for the one-particle distribution function.

Formulated a generalized Fokker-Planck equation for hydrodynamic variables.

Calculated the structure function of hydrodynamic fluctuations in cumulant form.

Abstract

Using the method of nonequilibrium statistical operator by Zubarev, an approach is proposed for the description of kinetics which takes into account the nonlinear hydrodynamic fluctuations for a quantum Bose system. Non-equilibrium statistical operator is presented which consistently describes both the kinetic and nonlinear hydrodynamic processes. Both a kinetic equation for the nonequilibrium one-particle distribution function and a generalized Fokker-Planck equation for nonequilibrium distribution function of hydrodynamic variables (densities of momentum, energy and particle number) are obtained. A structure function of hydrodynamic fluctuations in cumulant representation is calculated, which makes it possible to analyse the generalized Fokker-Planck equation in Gaussian and higher approximations of the dynamic correlations of hydrodynamic variables which is important in describing the quantum turbulent processes.