Asymptotic Density of Eigenvalue Clusters for the Perturbed Landau Hamiltonian

Abstract

We consider the Landau Hamiltonian (i.e. the 2D Schroedinger operator with constant magnetic field) perturbed by an electric potential V which decays sufficiently fast at infinity. The spectrum of the perturbed Hamiltonian consists of clusters of eigenvalues which accumulate to the Landau levels. Applying a suitable version of the anti-Wick quantization, we investigate the asymptotic distribution of the eigenvalues within a given cluster as the number of the cluster tends to infinity. We obtain an explicit description of the asymptotic density of the eigenvalues in terms of the Radon transform of the perturbation potential V.

30 pages. The explicit dependence on B and V in Theorem 1.6 (i) - (ii) indicated. Typos corrected. To appear in Communications in Mathematical Physics

References in corpus (2)

• Spectral shift function for operators with crossed magnetic and electric fields
• The spectral density of the scattering matrix for high energies

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
• A Trace Formula for Long-Range Perturbations of the Landau Hamiltonian
• Eigenvalue clusters for the hemisphere Laplacian with variable Robin condition