On the Szeg\H{o} formulas for truncated Wiener-Hopf operators

TL;DR

This paper extends Szeg\

Contribution

It generalizes Szeg\

Findings

Extended asymptotic formulas to non-smooth functions and domains.

Analyzed the scaling limit of bipartite entanglement entropy.

Provided new insights into Wiener-Hopf operators in quantum physics.

Abstract

We consider functions of multi-dimensional versions of truncated Wiener--Hopf operators with smooth symbols, and study the scaling asymptotics of their traces. The obtained results extend the asymptotic formulas obtained by H. Widom in the 1980's to non-smooth functions, and non-smooth truncation domains. The obtained asymptotic formulas are used to analyse the scaling limit of the spatially bipartite entanglement entropy of thermal equilibrium states of non-interacting fermions at positive temperature.