The system of interacting polaritons: Classical versus quantum kinetic equation

We derive the set of quantum kinetic equations for the system of interacting exciton polaritons in microcavities relaxing the Born-Markov approximation. We demonstrate the crucial role played by the nonclassical four particle correlators in the dynamics. The decoherence process is shown to be responsible for the transition from quantum to classical limit. The general formalism is applied for description of the dynamics of the polariton parametric oscillator.