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

Journal article, 2009

We study the Schrodinger operator with a constant magnetic field in the exterior of a compact domain in R-2d, 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.