Delocalization for Random Landau Hamiltonians with Unbounded Random Variables

2009/02/25 by François Germinet, Abel Klein, Germinet, François +3
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.0902.4300

arxiv created 2009/02/25 · arxiv updated 2009/12/01

Abstract

In this note we prove the existence of a localization/delocalization transition for Landau Hamiltonians randomly perturbed by an electric potential with unbounded amplitude. In particular, with probability one, no Landau gaps survive as the random potential is turned on, the gaps close, filling up partly with localized states. A minimal rate of transport is exhibited in the region of delocalization. To do so, we exploit the a priori quantization of the Hall conductance and extend recent Wegner estimates to the case of unbounded random variables.

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