Weakly coupled bound states of Pauli operators

TL;DR

This paper analyzes the spectral properties of a two-dimensional Pauli operator with a weakly attractive potential, revealing additional eigenvalues influenced by magnetic flux and providing their asymptotic behavior.

Contribution

It demonstrates the existence of extra eigenvalues in the weak coupling limit, depending on magnetic flux, and computes their asymptotics, extending understanding of Pauli operators with magnetic fields.

Findings

Additional eigenvalues depend on the magnetic flux being integer or not.

Eigenvalues appear for arbitrarily small coupling strengths.

Asymptotic formulas for eigenvalues are derived.

Abstract

We consider the two-dimensional Pauli operator perturbed by a weakly coupled, attractive potential. We show that besides the eigenvalues arising from the Aharonov-Casher zero modes there are two or one (depending on whether the flux of the magnetic field is integer or not) additional eigenvalues for arbitrarily small coupling and we calculate their asymptotics in the weak coupling limit.