Absence of mobility edge for the Anderson random potential on tree graphs at weak disorder
Mathematical Physics
2013-01-21 v1 Disordered Systems and Neural Networks
math.MP
Abstract
Our recently established criterion for the formation of extended states on tree graphs in the presence of disorder is shown to have the surprising implication that for bounded random potentials, as in the Anderson model, there is no transition to a spectral regime of Anderson localization, in the form usually envisioned, unless the disorder is strong enough.
Keywords
Cite
@article{arxiv.1109.2210,
title = {Absence of mobility edge for the Anderson random potential on tree graphs at weak disorder},
author = {Michael Aizenman and Simone Warzel},
journal= {arXiv preprint arXiv:1109.2210},
year = {2013}
}