Dynamics of superradiant processes in two-level macroscopic systems in a crystal

Method of partial elimination of boson variables is used to obtain an exact hierarchy of kinetic equations for a two-level crystalline system interacting with an electromagnetic field taking into account photon scattering on phonons. It is shown that the scattering on phonons reduces the time of hindrance of the superradiance momentum. Intensities of radiation with the fundamental, summary and difference frequencies are determined. Influence of radiation processes on the dynamics of the phonon subsystem is studied.