Boltzmann limit and quasifreeness for a homogenous Fermi gas in a weakly disordered random medium

Abstract

We discuss some basic aspects of the dynamics of a homogenous Fermi gas in a weak random potential, under negligence of the particle pair interactions. We derive the kinetic scaling limit for the momentum distribution function with a translation invariant initial state and prove that it is determined by a linear Boltzmann equation. Moreover, we prove that if the initial state is quasifree, then the time evolved state, averaged over the randomness, has a quasifree kinetic limit. We show that the momentum distributions determined by the Gibbs states of a free fermion field are stationary solutions of the linear Boltzmann equation; this includes the limit of zero temperature.