Sharp Spectral Asymptotics for Operators with Irregular Coefficients. V. Multidimensional Schroedinger operator with a strong magnetic field. Non-Full-rank case

TL;DR

This paper derives precise spectral asymptotics for multidimensional Schrödinger operators with strong magnetic fields under weak smoothness assumptions, focusing on cases where the magnetic intensity matrix has a constant defect.

Contribution

It extends previous work by providing more comprehensive results, including degenerations, for Schrödinger operators with irregular coefficients and constant defect in the magnetic intensity matrix.

Findings

Derived sharp spectral asymptotics under weak smoothness conditions

Analyzed degenerations of the magnetic intensity matrix

Improved and expanded previous results from version 1

Abstract

Sharp spectral asymptotics for multidimensional Schroedinger operators with the strong magnetic field are derived under rather weak smoothness conditions. I assume that magnetic intensity matrix has constant defect r>0 at each point. In comparison with version 1 of 5.5 year ago this version contains more results (we also study some degenerations), improvements and some minor corrections.