Sharp spectral estimates for the perturbed Landau Hamiltonian with $L^p$ potentials

Abstract

We establish a sharp estimate on the size of the spectral clusters of the Landau Hamiltonian with $L^p$ potentials in two dimensions as the cluster index tends to infinity. In three dimensions, we prove a new limiting absorption principle as well as a unique continuation theorem. The results generalize to higher dimensions.

10 pages