Absolute continuity of the spectrum of a Landau Hamiltonian perturbed by a generic periodic potential

Abstract

Consider $\Gamma$, a non-degenerate lattice in $\R^2$ and a constant magnetic field $B$ with a flux though a cell of $\Gamma$ that is a rational multiple of $2\pi$. We prove that for a generic $\Gamma$-periodic potential $V$, the spectrum of the Landau Hamiltonian with magnetic field $B$ and periodic potential $V$ is purely absolutely continuous.