Eigenvalue asymptotics of the even-dimensional exterior Landau-Neumann Hamiltonian

TL;DR

This paper investigates the eigenvalue distribution of the exterior Landau-Neumann Hamiltonian in even dimensions, providing asymptotic formulas for eigenvalue accumulation near Landau levels, especially for Reinhart domains.

Contribution

It derives new asymptotic formulas for eigenvalue accumulation in the exterior Landau-Neumann problem, including precise results for Reinhart domains.

Findings

Eigenvalues cluster around Landau levels with specific asymptotic rates.

Asymptotic formulas are established for eigenvalue accumulation.

More precise asymptotics are obtained for Reinhart domains.

Abstract

We study the Schroedinger operator with a constant magnetic field in the exterior of a compact domain in $\mathbb{R}^{2d}$, $d\geq 1$. 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 Reinhart domain we are able to show a more precise asymptotic formula.