Eigenvalue clusters of the Landau Hamiltonian in the exterior of a compact domain

TL;DR

This paper studies the eigenvalue clusters of the Landau Hamiltonian outside a compact domain, analyzing how eigenvalues accumulate around Landau levels in the presence of a magnetic field.

Contribution

It provides a detailed analysis of the accumulation rate of eigenvalues in clusters near Landau levels for the Schrödinger operator with magnetic field outside a compact domain.

Findings

Eigenvalues form clusters around Landau levels.

The rate of eigenvalue accumulation in clusters is characterized.

Results enhance understanding of spectral properties in magnetic quantum systems.

Abstract

We consider the Schrodinger operator with a constant magnetic field in the exterior of a compact domain on the plane. The spectrum of this operator consists of clusters of eigenvalues around the Landau levels. We discuss the rate of accumulation of eigenvalues in a fixed cluster.