Semiclassical spectrum of the Dirichlet-Pauli operator on an annulus

TL;DR

This paper provides a detailed semiclassical analysis of the Dirichlet-Pauli operator's spectrum on an annulus with a positive radial magnetic field, revealing explicit asymptotics and the Aharonov-Bohm effect.

Contribution

It offers the first explicit first-order asymptotic expansion of the lowest eigenvalues for this operator in the semiclassical limit, highlighting the Aharonov-Bohm effect.

Findings

Explicit asymptotic expansion of lowest eigenvalues

Revealed the Aharonov-Bohm effect in this context

Analyzed the spectrum under radial magnetic fields

Abstract

This paper is devoted to the semiclassical analysis of the spectrum of the Dirichlet-Pauli operator on an annulus. We assume that the magnetic field is strictly positive and radial. We give an explicit asymptotic expansion at the first order of the lowest eigenvalues of this operator in the semiclassical limit. In particular, we exhibit the Aharonov-Bohm effect that has been revealed, for constant magnetic field, in a recent paper by Helffer and Sundqvist.