Stochastic dynamics of microcavity polaritons

We study the time dependent polariton condensation as well as the parametric scattering process of polaritons in a semiconductor microcavity. Based upon a new stochastic scheme the dynamics for both cases is fully analyzed. We show how the evolution of the system is described by a set of stochastic differential Schrِdinger equations which on average reproduces the exact dynamics. Furthermore, we underline the role that Coulomb correlations plays in the polariton dynamics. Threshold behaviors are well captured by the present approach. The results are in complete agreement with recent experimental observations.