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

Frédéric Klopp (1)

1 LAGA - Laboratoire Analyse, Géométrie et Applications

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.

Mots clés: Landau Hamiltonian; periodic perturbation; absolutely continuous spectrum

Domaines: Physique mathématique [math-ph]

Frédéric Klopp. Absolute continuity of the spectrum of a Landau Hamiltonian perturbed by a generic periodic potential. 2009. ⟨hal-00376643⟩