On non-perturbative solution of quantum BBGKY hierarchy

Abstract

We consider some approaches to the construction of a non-perturbative solution of the Cauchy problem of the quantum BBGKY hierarchy for a sequence of marginal density operators and analyze its properties for initial data from the space of sequences of trace class operators. One is represented in the form of a series expansion over particle subsystems which generating operators are the corresponding-order cumulants of the groups of operators of systems of finitely many quantum particles.