P. A. Hlushak, M. V. Tokarchuk
Using the method of non-equilibrium statistical Zubarev operator an approach to the description of kinetics taking into account the nonlinear hydrodynamic fluctuations for quantum Bose system is proposed. The non-equilibrium statistical operator that consistently describes both the kinetic and nonlinear hydrodynamic fluctuations in quantum liquid is calculated. A kinetic equation for the non-equilibrium one-particle distribution function and generalized Fokker-Planck equation for non-equilibrium distribution function of hydrodynamic variables: densities of momentum, energy and particle numbers are obtained. A structural function of hydrodynamic fluctuations in cumulant representation is calculated. It provides a possibility to analyzing the generalized Fokker-Planck equation in Gaussian and higher approximations for dynamic correlations of hydrodynamic variables that is important to describe the quantum turbulent processes. The generalized Gross-Pitaevkii equation for the order parameter which takes into account nonlinear hydrodynamic fluctuations is obtained.
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http://arxiv.org/abs/1301.0481
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