Global trace asymptotics in the self-generated magnetic field in the case of Coulomb-like singularities

TL;DR

This paper derives precise semiclassical trace asymptotics for a 3D Schrödinger operator with self-generated magnetic fields and Coulomb-like singularities, including a Scott correction, improving previous results.

Contribution

It provides an improved and simplified analysis of trace asymptotics with Scott correction for operators with Coulomb singularities and self-generated magnetic fields.

Findings

Weyl law with Scott correction for Coulomb singularities

Error estimate of O(h^{-4/3}) under certain conditions

Enhanced understanding of magnetic field effects in semiclassical limits

Abstract

We consider a semiclassical asymptotics of local trace for the 3D-Schroedinger operator with self-generated magnetic field in the case when electric potential has one or several Coulomb-like singularities; it is given by Weyl expression plus (magnetic) Scott correction term with O(h^{-4/3}) error provided distance between singularities is large enough. Significant improvement and simplification in comparison to v1.