Український математичний конгрес - 2009

Жанна Цвір (Київський національний університет імені Тараса Шевченка, Україна)

On solution of kinetic cluster expansions

The main objective of the work is the investigation of the kinetic claster expansions of cumulants of groups of scattering operators of the von Neumann equations for quantum many-particle systems.

We construct the solutions of formulated kinetic cluster expansions.

Using obtained results we prove the convergence of series of the functionals, represented by the correlation marginal density operators in the space of trace class operators. Such functionals are the base for the rigorous derivation of quantum kinetic equations from underlying many-particle dynamics.