V.I. Gerasimenko (Institute of Mathematics, Kyiv)
V.V. Krechko (Institute of Mathematics, Kyiv)

On solution expansions of hierarchies of evolution equations for quantum many-particle systems

Abstract:
We consider approaches to the construction of a non-perturbative solution of the Cauchy problem of the quantum BBGKY hierarchies of evolution equations for quantum many-particle systems. In particular,using constructed non-perturbative solution forastate of quantum many-particle systems composed of a tracer particle and an environment,which is a system of a non-fixed number of identical quantum particles, for some classes of initial states we prove an equivalence of the description of the evolution of states governed by the quantum BBGKY hierarchy and the generalized quantum Fokker–Planck kinetic equation. Thus, an alternative method of the description of the evolution of a tracer quantum particle in an environment is given by the established quantum Fokker–Planck kinetic equation.