Nonequilibrium Green's function for high electric fields in semiconductors

We develop a formalism, for studying the motion of non-degenerate electrons in semiconductors, which allows a non-perturbative description of the effects of an external high electric field on electron-phonon scattering within the Kadanoff-Baym-Keldysh non-equilibrium Green's function approach. Recognizing that high fields break a translation symmetry of the system and that momentum is no longer a good quantum number, we use Airy transforms to handle the position dependence parallel to the applied high field. Based on the exact solutions of Schrodinger's equation, we solve Dyson's equation for the single-particle retarded Green's function G...