Master kinetic equation for a particle in the field of randomly varying scatterers

A study is made of the quantum-mechanical scattering of a particle in the potential field of a collection of scatterers whose positions in space and switching-on times are distributed randomly. On the basis of the method of solution of the stochastic Liouville–von Neumann equation developed earlier by one of the authors, a kinetic equation (of the type of the Pauli equation) for the diagonal elements of the density matrix of the particle is derived under the condition of a homogeneous distribution of the scatterers in space. Rigorous inequaI ties are obtained that determine the accuracy of the kinetic equation, and from these there follow limiting conditions on its applicability for describing relaxation and scattering processes.