On the Spectral Properties of the Landau Hamiltonian Perturbed by a moderately Decaying Magnetic Field

Abstract

The Landau Hamiltonian, describing the behavior of a quantum particle in dimension 2 in a constant magnetic field, is perturbed by a magnetic field with power-like decay at infinity and a similar electric potential. We describe how the spectral subspaces change and how the Landau levels split under this perturbation.