Delocalization for Random Landau Hamiltonians with Unbounded Random Variables
Mathematical Physics
2009-02-26 v1 math.MP
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.
Keywords
Cite
@article{arxiv.0902.4300,
title = {Delocalization for Random Landau Hamiltonians with Unbounded Random Variables},
author = {François Germinet and Abel Klein and Benoît Mandy},
journal= {arXiv preprint arXiv:0902.4300},
year = {2009}
}