Boltzmann limit for a homogenous Fermi gas with dynamical Hartree-Fock interactions in a random medium

TL;DR

This paper investigates the behavior of a homogenous Fermi gas with dynamical Hartree-Fock interactions in a random medium, deriving Boltzmann limits under various scaling regimes of potential and interaction strength.

Contribution

It establishes the Boltzmann limits for a Fermi gas with dynamical Hartree-Fock interactions in a random medium across different scaling regimes.

Findings

Derived Boltzmann limits for different regimes

Analyzed effects of weak static random potential

Connected interaction strength with kinetic behavior

Abstract

We study the dynamics of the thermal momentum distribution function for an interacting, homogenous Fermi gas on $\Z^3$ in the presence of an external weak static random potential, where the pair interactions between the fermions are modeled in dynamical Hartree-Fock theory. We determine the Boltzmann limits associated to different scaling regimes defined by the size of the random potential, and the strength of the fermion interactions.