On the semiclassical regularity of thermal equilibria

TL;DR

This paper investigates the regularity of fermionic thermal equilibrium states, establishing semiclassical bounds and identifying specific states that meet certain regularity criteria, advancing understanding of finite-temperature quantum systems.

Contribution

It provides new semiclassical bounds for fermionic equilibrium states and explicitly characterizes states satisfying prior regularity assumptions.

Findings

Fermionic equilibrium states satisfy semiclassical bounds at positive temperature

Explicit identification of states meeting regularity assumptions

Advances understanding of quantum statistical mechanics at finite temperature

Abstract

We study the regularity properties of fermionic equilibrium states at finite positive temperature and show that they satisfy certain semiclassical bounds. As a corollary, we identify explicitly a class of positive temperature states satisfying the regularity assumptions of [J.J. Chong, L. Lafleche, C. Saffirio: arXiv:2103.10946 (2021)].