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

TL;DR

This paper analyzes the dynamics of a homogeneous Fermi gas in a weak disordered medium, deriving a linear Boltzmann equation for the momentum distribution and showing quasifreeness preservation in the kinetic limit.

Contribution

It establishes the kinetic scaling limit for a Fermi gas in a random potential and proves quasifreeness is maintained in the averaged kinetic limit for initial quasifree states.

Findings

Derivation of a linear Boltzmann equation for the momentum distribution.

Proof that quasifree initial states lead to quasifree kinetic limits.

Identification of stationary solutions as Gibbs states of a free fermion field.

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.