Tsvir Z. Quantum kinetic nonlinear equations

The thesis is devoted to the problem to justification of the derivation of quantum kinetic equations. In the thesis the method of kinetic cluster expansions of the cumulants of groups of operators of quantum systems is developed. This method defines rigorous expansions of marginal functionals of states of quantum systems of the particles that describe all possible states of quantum many particle systems in terms of one-particle density operator. The equivalence of the description of evolution of states of statistical systems by means of the Cauchy problem of the hierarchy of BBGKY quantum equations and the Cauchy problem for generalized quantum kinetic equation and a sequence of explicity defined functional of states is established. The existence theorem about of the strong and weak solutions of the Cauchy problem of the generalized quantum kinetic equation in the space of trace class operators is proved and their properties are investigated.