DELOCALIZATION FOR RANDOM LANDAU HAMILTONIANS WITH UNBOUNDED RANDOM VARIABLES

François Germinet (1) , Abel Klein (2) , Benoît Mandy (1)

1 AGM - UMR 8088 - Analyse, Géométrie et Modélisation
2 Departement of Mathematics

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.

Mots clés: Disordered systems; Random operators; Random operators and equations

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

François Germinet, Abel Klein, Benoît Mandy. DELOCALIZATION FOR RANDOM LANDAU HAMILTONIANS WITH UNBOUNDED RANDOM VARIABLES. 2009. ⟨hal-00363145⟩