Absolutely continuous spectrum for a random potential on a tree with strong transverse correlations and large weighted loops
Mathematical Physics
2015-05-13 v1 math.MP
Spectral Theory
Abstract
We consider random Schr\"odinger operators on tree graphs and prove absolutely continuous spectrum at small disorder for two models. The first model is the usual binary tree with certain strongly correlated random potentials. These potentials are of interest since for complete correlation they exhibit localization at all disorders. In the second model we change the tree graph by adding all possible edges to the graph inside each sphere, with weights proportional to the number of points in the sphere.
Cite
@article{arxiv.0809.4197,
title = {Absolutely continuous spectrum for a random potential on a tree with strong transverse correlations and large weighted loops},
author = {Richard Froese and David Hasler and Wolfgang Spitzer},
journal= {arXiv preprint arXiv:0809.4197},
year = {2015}
}
Comments
25 pages, 4 figures