On the semi-classical analysis of the groundstate energy of the Dirichlet Pauli operator in non-simply connected domains

TL;DR

This paper analyzes the ground state energy of the Dirichlet Pauli operator in non-simply connected planar domains, showing it becomes exponentially small as the semi-classical parameter approaches zero and providing decay rate estimates.

Contribution

It extends previous results to non-simply connected domains, providing new estimates for the exponential decay of the ground state energy in the semi-classical limit.

Findings

Ground state energy is exponentially small as the semi-classical parameter tends to zero.

Provides estimates for the decay rate of the ground state energy.

Extends prior work to include non-simply connected domains.

Abstract

We consider the Dirichlet Pauli operator in bounded connected domains in the plane, with a semi-classical parameter. We show, in particular, that the ground state energy of this Pauli operator will be exponentially small as the semi-classical parameter tends to zero and estimate this decay rate. This extends our results, discussing the results of a recent paper by Ekholm--Kova\v{r}\'ik--Portmann, to include also non-simply connected domains.