Kinetics of partially coherent polaritons in semiconductors

A derivation of the equations describing kinetic and dynamic properties of a high-density polariton system excited in direct-gap semiconductors by an external laser field is given. The Keldysh diagram technique for non-equilibrium processes formulated in terms of functional equations is used. With functional Legendre transformation, Dyson equations are derived for normal and abnormal connected Keldysh-Green's functions, which describe quantum fluctuations in the system, and also for a coherent part of the polariton field. The vertices in the Dyson equation are calculated using perturbation theory. Boltzmann-type kinetic equations for the case of small time inhomogeneity of the system are obtained in Born approximation.