Generalized balance equations for anelectron-phonon system

A new model, based on an asymptotic procedure for solving the generalized kinetic equations of electrons and phonons, is proposed, which gives naturally the displaced Maxwellian at the leading order. The balance equations for the electron number, total energy density and total momentum for the whole system constitute now, together with Poisson equation, a system of four equations for the electron chemical potential, the temperature of the system, the drift velocity and the electric potential. In the drift-diffusion approximation the constitutive laws are derived and the Onsager relations recovered