On the kinetics of subsystems interacting with Bosons

A closed Markovian equation for the density matrix of a subsystem interacting with a boson field is obtained. Boson amplitudes are exclued from this equation. The generalized Boltzmann equation for the case of the weak electron-phonon interaction, the kinetic equation for the density matrix and the Fokker-Planck equation for the distribution function of the polaron in the Feynman model (arbitrary coupling) and the Thornber-Feynman result for nonlinear conductivity in polar crystals are obtained with the aid of corresponding approximations for the subsystem dynamics in the equation obtained. A possibility for the calculation of corrections to the Boltzmann equation is shown.