Semiclassical spectrum of the Dirichlet–Pauli operator on an annulus

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 a constant magnetic field, in a recent paper by Helffer and Sundqvist.