Virtual bound states of the Pauli operator with an Aharonov-Bohm potential

TL;DR

This paper investigates the spectral properties of the two-dimensional Pauli operator with an Aharonov-Bohm magnetic field, revealing criticality and deriving eigenvalue asymptotics under electric perturbations.

Contribution

It demonstrates the critical nature of both components of the Pauli operator with Aharonov-Bohm potential and derives eigenvalue asymptotics for weak electric perturbations.

Findings

Both components of the Pauli operator are critical.

Asymptotics of weakly coupled eigenvalues are derived.

Contrasts with regular magnetic potential cases.

Abstract

A maximal realisation of the two-dimensional Pauli operator, subject to Aharonov--Bohm magnetic field, is investigated. Contrary to the case of the Pauli operator with regular magnetic potentials, it is shown that both components of the Pauli operator are critical. Asymptotics of the weakly coupled eigenvalues, generated by electric (not necessarily self-adjoint) perturbations, are derived.