Condensed Matter Physics, 2006, vol. 9, No. 3(47), p. 415430, English
DOI:10.5488/CMP.9.3.415
Title:
Reduced description of nonequilibrium processes and correlation
functions. Divergences and nonanalyticity
Author(s):
 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 nonanalytic 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, 05.30d
