Projection approach for composite open quantum systems

This report presents the application of the Nakajima–Zwanzig projection method to the derivation of kinetic equations for systems treated as weakly interacting open subsystems. As illustrative examples, we analyze the Jaynes–Cummings model with dissipation and the spontaneous parametric down-conversion model involving two dissipative modes. For both systems, the approach enables a systematic derivation of corrections to the parametric approximation by accounting for quantum depletion of the pumping field.