On the Szegő formulas for truncated Wiener-Hopf operators
arXiv:1801.02520 · doi:10.1007/s00020-018-2500-4
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.
28 pages