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arXiv · 1907.11492

Pseudo-gaps for random hopping models

Florian Dorsch·Hermann Schulz-Baldes
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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.

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BibTeXRIS

Florian Dorsch, Hermann Schulz-Baldes. 2019-07-26. Pseudo-gaps for random hopping models. https://doi.org/10.1088/1751-8121%2Fab5e8c

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