On the semiclassical spectrum of the Dirichlet-Pauli operator

TL;DR

This paper provides semiclassical estimates for the eigenvalues of the Dirichlet-Pauli operator on bounded domains, establishing eigenvalue simplicity and asymptotic behavior under positive magnetic fields.

Contribution

It introduces new asymptotic estimates for the eigenvalues of the Dirichlet-Pauli operator using Segal-Bargmann and Hardy space techniques, assuming positive magnetic fields.

Findings

Eigenvalues are simple under generic conditions.

Asymptotic estimates involve Segal-Bargmann and Hardy spaces.

Results apply to magnetic fields that are positive and satisfy certain conditions.

Abstract

This paper is devoted to semiclassical estimates of the eigenvalues of the Pauli operator on a bounded open set whose boundary carries Dirichlet conditions. Assuming that the magnetic field is positive and a few generic conditions, we establish the simplicity of the eigenvalues and provide accurate asymptotic estimates involving Segal-Bargmann and Hardy spaces associated with the magnetic field.