Nonperturbative balance equations for the nonequilibrium electron-phonon-impurity system in an applied high electric field

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Abstract
Energy-momentum balance equations are derived for the nonequilibrium system consisting of many electrons plus lattice impurities in an applied electric field with electron phonon and electron-impurity as well as applied field interactions treated nonperturbatively. After carrying out the path integration to eliminate the phonon variables and the ensemble average over the impurity configurations exactly, the balance equations derived could be expressed in terms of generic nonequilibrium Green’s functions. Since the theory is in a locally space-time-dependent form, it applies either to the uniform, steady system or the space-time-dependent system. The physical interpretation of these balance equations and their connection to other approaches are also discussed.