Condensed Matter Physics, 2006, vol. 9, No. 3(47), p. 415-430, English

Title: Reduced description of nonequilibrium processes and correlation functions. Divergences and non-analyticity
  A.I.Sokolovsky (Dnipropetrovs'k National University, 13, Naukova St., Dnipropetrovs'k, 49050, Ukraine)

A complete theory for investigation of time correlation functions is developed on the basis of the Bogolyubov reduced description method proceeding from his functional hypothesis. The problem of convergence in the theory of nonequilibrium processes and its relation to the non-analytic dependence of basic values of the theory on a small parameter of the perturbation theory are discussed. A natural regularization of integral equations of the theory is proposed. In the framework of a model of slow variables (hydrodynamics of a fluid, kinetics of a gas) a generalized perturbation theory without divergencies is constructed corresponding to a partial summation in a usual perturbation theory. Properties of Green functions are discussed on the basis of resolvent formalism for the Liouville operator. A generalized Ernst and Dorfman theory is elaborated allowing to study the peculiarities of correlation and Green functions and to solve the convergence problem in the reduced description method.

Key words: reduced description of nonequilibriun processes, functional hypothesis, convergence problem, natural regularization, asymptotics of time correlation functions, Green functions, peculiarities of correlation and Green functions, generalized Ernst and Dorfman theory
PACS: 05.20.Dd, 05.30-d

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