Toward polaron kinetics in the Bogoliubov reduced description method

In the framework of the Bogoliubov method of reduced description of nonequilibrium states, which is based on his functional hypothesis, we obtain a kinetic equation for arbitrary inhomogeneous electron states in a polar crystal in the presence of a strong electric field. Using the reduced description method, we study the equalization of velocities and temperatures of the polaron gas with a small density and the phonon subsystem in the presence of a weak electric field in the spatially homogeneous case. We establish that the nonequilibrium distribution function of a polaron differs from the Maxwell distribution even in the approximation that is linear in small differences between the subsystem velocities and temperatures. We calculate the corresponding relaxation times and polaron mobility.