Nonequilibrium green's functions and kinetic equations for highly excited semiconductors

Aiming at a realistic description of highly excited states in semiconductors the derivation of kinetic equations is reformulated where emphasis is laid on the consideration of many-body effects without perturbation expansion arguments. By the variational derivation technique a set of equations for the Green's functions and the self-energy is obtained, which is formally closed and should be an appropriate starting point for any kind of iteration or approximation. The connection of this technique with the diagram technique given by Keldysh and the translation technique for thermodynamic Green's functions according to Kadanoff and Baym is demonstrated. The general equations are then exactly transformed to difference and sum coordinates, enabling an adequate approximation in the case of slowly varuing (in space and time) external fields in terms of local quantities. In linear approximation with respect to the drift operator D̂ a generalized Boltzmann equation is derived, which clearly exhibits many-body effects in all drift and collision contributions.