Quantum Statistical Derivation of Rate Equations for Electronic Processes in Polar Crystals with External Electric Field

Applying the Nakajima-Zwanzig method to the von Neumann equation of a system of interacting electrons and nuclei, etc., and evaluating the Pauli-Master equation according to RieckersStumpf, we obtain a system of reaction equations for electron-phonon-photon processes in a polar crystal. Further elaboration of these reaction equations leads to rate equations for electrons which include impurity center processes as well as conduction band processes in an external electric field. If the conduction band processes run faster than the other processes, the rate equations can be reduced to a Boltzmann equation with drift term for the conduction electrons, coupled to rate equations for impurity center electrons where the number of conduction electrons must not be conserved. Furthermore, the basic problem of electronic state formation in external fields is discussed, the corresponding interaction terms are derived and a functional for the calculation of "bound" states in external fields is given.