Dynamical delocalization in random Landau Hamiltonians

Abstract

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.

Authors

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