Homogenization and Hydrodynamic Limit for Fermi-Dirac Statistics Coupled to a Poisson Equation

This paper deals with the diffusion approximation of a Boltzmann-Poisson system modeling Fermi-Dirac statistics in the presence of an extra external oscillating electrostatic potential. Here we extend the analysis done in [19] to the case of a nonlinear collision operator. In addition to the averaging lemma and control from entropy dissipation used in [19], here we use two-scale Young measures and renormalization techniques to prove the convergence. This result rigorously justifies the formal analysis of [3].