Low-frequency correlation functions in case of nonlinear dynamics of fluctuations

A method is developed for calculating low-frequency asymptotic correlation functions of basic operators “âm” which correspond to gross variables describing a nonequibliriium state of a system. We have introduced a Weyl operator, its nonequilibrium average value being considered as a quantum distribution function of gross variables. The generalized Fokker-Planck equation is then derived for the distribution function. This equation is used for obtaining a chain of equations for asymptotic correlation functions containing only Weyl operator functions of “âm”. The kinetic coefficients and self-energy are expressed in terms of irreducible correlation functions which correspond to effects of nonlinear dynamics of fluctuations. It is shown in our approach that hydrodynamic modes may be considered as a zero order approximation. As an application of the formalism the generalized mode-mode coupling approximation is investigated.