Weak coupling asymptotics for the Pauli operator in two dimensions

TL;DR

This paper derives asymptotic formulas for the negative eigenvalues of the two-dimensional Pauli operator with a weak potential, extending previous results to non-radial magnetic fields and potentials.

Contribution

It generalizes prior work by removing the radial symmetry restriction, providing new asymptotic expansions for the eigenvalues in more general magnetic field configurations.

Findings

Derived asymptotic expansions for negative eigenvalues

Extended results to non-radial magnetic fields and potentials

Enhanced understanding of spectral properties of the Pauli operator

Abstract

We compute asymptotic expansions for the negative eigenvalues of the Pauli operator in two dimensions perturbed by a weakly coupled potential with definite sign. Whereas previous results were limited to the case of radial magnetic fields and potentials, we are able to drop the assumption of radial symmetry entirely.