Semiclassical spectrum of the Dirichlet-Pauli operator on an annulus
Spectral Theory
2022-05-31 v1 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.2205.15152,
title = {Semiclassical spectrum of the Dirichlet-Pauli operator on an annulus},
author = {Enguerrand Lavigne Bon},
journal= {arXiv preprint arXiv:2205.15152},
year = {2022}
}