Dynamical delocalization in random Landau Hamiltonians


We prove the existence of dynamical delocalization for random Landau Hamiltonians near each Landau level. Since typically there is dynamical localization at the edges of each disordered-broadened Landau band, this implies the existence of at least one dynamical mobility edge at each Landau band, namely a boundary point between the localization and delocalization regimes, which we prove to converge to the corresponding Landau level as either the magnetic field goes to infinity or the disorder goes to zero.


François Germinet

Département de Mathématiques, Université de Cergy-Pontoise, 95302 Cergy-Pontoise, France

Abel Klein

Department of Mathematics, University of California, Irvine, CA 92697, United States

Jeffrey H. Schenker

Department of Mathematics, Michigan State University, East Lansing, MI 48824, United States