The Altshuler-Shklovskii Formulas for Random Band Matrices I: the Unimodular Case
Abstract
We consider the spectral statistics of large random band matrices on mesoscopic energy scales. We show that the two-point correlation function of the local eigenvalue density exhibits a universal power law behaviour that differs from the Wigner-Dyson-Mehta statistics. This law had been predicted in the physics literature by Altshuler and Shklovskii [4]; it describes the correlations of the eigenvalue density in general metallic samples with weak disorder. Our result rigorously establishes the Altshuler-Shklovskii formulas for band matrices. In two dimensions, where the leading term vanishes owing to an algebraic cancellation, we identify the first non-vanishing term and show that it differs substantially from the prediction of Kravtsov and Lerner [33].
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Cite
@article{arxiv.1309.5106,
title = {The Altshuler-Shklovskii Formulas for Random Band Matrices I: the Unimodular Case},
author = {Laszlo Erdos and Antti Knowles},
journal= {arXiv preprint arXiv:1309.5106},
year = {2015}
}