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

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.

Chain of kinetic equations for the distribution functions of particles in simple liquid taking into account nonlinear hydrodynamic fluctuations

“…whereṅ k = iL Nnk ,J k = iL NĴk ,ε k = iL Nεk , the last expression in (14) can be rewritten in following form:…”

“…The study of nonlinear kinetic and hydrodynamic fluctuations in dense gases, liquids and plasma, in turbulence phenomena and dynamics of phase transitions, in chemical reactions and self-organizing processes are relevant both on kinetic and hydrodynamic levels of description in statistical theory of non-equilibrium processes [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]. The non-equilibrium states of such systems are far from equilibrium.…”