Pseudo-gaps for random hopping models
Mathematical Physics
2020-06-24 v2 Disordered Systems and Neural Networks
math.MP
Abstract
For one-dimensional random Schr\"odinger operators, the integrated density of states is known to be given in terms of the (averaged) rotation number of the Pr\"ufer phase dynamics. This paper develops a controlled perturbation theory for the rotation number around an energy, at which all the transfer matrices commute and are hyperbolic. Such a hyperbolic critical energy appears in random hopping models. The main result is a H\"older continuity of the rotation number at the critical energy that, under certain conditions on the randomness, implies the existence of a pseudo-gap. The proof uses renewal theory. The result is illustrated by numerics.
Cite
@article{arxiv.1907.11492,
title = {Pseudo-gaps for random hopping models},
author = {Florian Dorsch and Hermann Schulz-Baldes},
journal= {arXiv preprint arXiv:1907.11492},
year = {2020}
}
Comments
minor corrections, published in J.Phys.A