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

Abstract

We study the Schroedinger operator with a constant magnetic field in the exterior of a compact domain in ${\mathbb{R}}^{2d}$, $d\ge 1$. 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.

References in corpus (4)

• Quasi-classical versus non-classical spectral asymptotics for magnetic Schroedinger operators with decreasing electric potentials
• Spectral asymptotics of Pauli operators and orthogonal polynomials in complex domains
• Magnetic edge states
• Discrete spectrum distribution of the Landau Operator Perturbed by an Expanding Electric Potential

Cited by in corpus (4)

• Very weak solutions of wave equation for Landau Hamiltonian with irregular electromagnetic field
• Wave equation for operators with discrete spectrum and irregular propagation speed
• Threshold singularities of the spectral shift function for geometric perturbations of magnetic Hamiltonians
• Counting function of magnetic resonances for exterior problems