Level statistics for one-dimensional Schr\"odinger operators and Gaussian beta ensemble
Mathematical Physics
2015-06-18 v1 math.MP
Abstract
We study the level statistics for two classes of 1-dimensional random Schr\"odinger operators : (1) for operators whose coupling constants decay as the system size becomes large, and (2) for operators with critically decaying random potential. As a byproduct of (2) with our previous result \cite{KN} imply the coincidence of the limits of circular and Gaussian beta ensembles.
Keywords
Cite
@article{arxiv.1312.6901,
title = {Level statistics for one-dimensional Schr\"odinger operators and Gaussian beta ensemble},
author = {Fumihiko Nakano},
journal= {arXiv preprint arXiv:1312.6901},
year = {2015}
}