Eigenvalue Asymptotics of the Even-Dimensional Exterior Landau-Neumann Hamiltonian

Abstract

We study the Schrödinger operator with a constant magnetic field in the exterior of a compact domain in ℝ2𝑑, 𝑑≥1. The spectrum of this operator consists of clusters of eigenvalues around the Landau levels. We give asymptotic formulas for the rate of accumulation of eigenvalues in these clusters. When the compact is a Reinhardt domain we are able to show a more precise asymptotic formula.