Kinetics of two-photon superradiance in the case of damped polarization

Dicke-type model with the interaction bilinear in field operators is considered. An exact hierarchy of kinetic equations is constructed which does not formally include dynamical Bose-operator. The elimination of Bose-operators is achieved using a conservation law for the model and a theorem about some special nonequilibrium averages. The theorem generalizes the well-known Bogoliubov lemma. It is proved under quite general conditions and is valid for the Bose as well as Fermi-operators. A nonequilibrium operator in these averages can be explicitely time-dependent or can have a multi-time form. A solution of the hierarchy in the case of damping polarisation shows that the pulse of the two-photon super-radiance in the small-sample system may fiave two commensurate maxima. The pulse of the one-photon super-radiance in such a system, as is well-known, has one maximum only.