Theory of stochastic processes in quantum dynamical systems

Stochastic process of the motion of trial particle in dynamical system with the pair short-range interaction potential is considered. Quantum generalisation of N. N. Bogoliubov's kinetic equation [1] is developed which leads to the nonexponential law of decreasing of the velocity correlation function of trial particle in the system of classical hard spheres at large time intervals. Stochastic perturbation theory with respect to small density as well as the renormalization of Green's function of trial particle and the collision operators for the Liouville equation are used for deriving the equation.