Kinetic theory and thermalization of weakly interacting fermions

TL;DR

This paper explores the kinetic theory of weakly interacting fermions, focusing on the Hubbard model with spin conservation and examining how kinetic processes relate to thermalization.

Contribution

It introduces a kinetic framework for the fermionic Hubbard model including spin conservation effects and analyzes the connection between kinetic equations and thermalization processes.

Findings

Derivation of a Vlasov-type term in the Boltzmann equation for the Hubbard model.

Insights into how kinetic theory describes thermalization in fermionic systems.

Extension of kinetic equations to account for spin conservation.

Abstract

Weakly interacting quantum fluids allow for a natural kinetic theory description which takes into account the fermionic or bosonic nature of the interacting particles. In the simplest cases, one arrives at the Boltzmann-Nordheim equations for the reduced density matrix of the fluid. We discuss here two related topics: the kinetic theory of the fermionic Hubbard model, in which conservation of total spin results in an additional Vlasov type term in the Boltzmann equation, and the relation between kinetic theory and thermalization.