On the Semiclassical Analysis of the Ground State Energy of the Dirichlet Pauli Operator in Non-Simply Connected Domains

Abstract

We consider the Dirichlet Pauli operator in bounded connected domains in the plane, with a semiclassical parameter. We show that the ground state energy of the Pauli operator is exponentially small as the semiclassical parameter tends to zero and estimate the decay rate. This extends our recent results discussing a recent paper by Ekholm–Kovařík–Portmann, including non-simply connected domains.