Theory of high-electric-field quantum transport for electron-resonant impurity systems

A formalism is developed which allows a nonperturbative calculation of the effects of the electric field on electron-impurity scattering. The single-site $T$ matrix is evaluated exactly and studied numerically for a model potential. For a dilute concentration of random impurities, the impurity-averaging procedure is carried out in a finite external field and a nonlinear integral equation is derived for the Green function. This equation is solved in an approximate, but consistent, manner. Finally, a quantum-transport equation is constructed with the generalized Baym-Kadanoff method of nonequilibrium quantum statistical mechanics. Special attention is paid to the field dependence of the collision integral. In particular, in the limit of slow spatial variations, a Boltzmann-type transport equation is derived with a nonlocal field-dependent collision integral.