Poisson statistics for 1d Schr\"odinger operators with random decaying potentials
Mathematical Physics
2017-09-12 v2 math.MP
Probability
Abstract
We consider the 1d Schr\"odinger operators with random decaying potentials where the spectrum is pure point(sub-critical case). We show that the point process composed of the rescaled eivenvalues, together with those zero points of the corresponding eigenfunctions, converges to the Poisson process.
Keywords
Cite
@article{arxiv.1605.02416,
title = {Poisson statistics for 1d Schr\"odinger operators with random decaying potentials},
author = {Shinichi Kotani and Fumihiko Nakano},
journal= {arXiv preprint arXiv:1605.02416},
year = {2017}
}