On the scattering problem for infinitely many fermions in dimensions $d\geq3$ at positive temperature

TL;DR

This paper investigates the scattering behavior of infinitely many fermions at positive temperature in dimensions three and higher, extending previous results to higher dimensions through improved analytical estimates.

Contribution

It introduces new Strichartz estimates that enable the analysis of fermion scattering in dimensions $d\,\geq\,3$, expanding upon prior work limited to lower dimensions.

Findings

Proved scattering for small perturbations around thermal equilibrium.

Extended results from 2D to higher dimensions $d\geq3$.

Developed improved Strichartz estimates for density operators.

Abstract

In this paper, we study the dynamics of a system of infinitely many fermions in dimensions $d\geq3$ near thermal equilibrium and prove scattering in the case of small perturbation around equilibrium in a certain generalized Sobolev space of density operators. This work is a continuation of our previous paper, and extends the important recent result of M. Lewin and J. Sabin of a similar type for dimension d=2. In the work at hand, we establish new, improved Strichartz estimates that allow us to control the case $d\geq3$.