Stability of a Szegő-type asymptotics

Abstract

We consider a multi-dimensional continuum Schrödinger operator $H$ which is given by a perturbation of the negative Laplacian by a compactly supported bounded potential. We show that, for a fairly large class of test functions, the second-order Szegő-type asymptotics for the spatially truncated Fermi projection of $H$ is independent of the potential and, thus, identical to the known asymptotics of the Laplacian.

Version as to appear in the special issue of J Math Phys dedicated to Abel Klein

References in corpus (1)

• On the Area Law for Disordered Free Fermions

Cited by in corpus (3)

• The Widom-Sobolev formula for discontinuous matrix-valued symbols
• Enhanced area law in the Widom-Sobolev formula for the free Dirac operator in arbitrary dimension
• An enhanced term in the Szegő-type asymptotics for the free massless Dirac operator