Lifschitz Tails for Random Schr\"{o}dinger Operator in Bernoulli Distributed Potentials
Mathematical Physics
2015-06-19 v1 math.MP
Abstract
This paper presents an elementary proof of Lifschitz tail behavior for random discrete Schr\"{o}dinger operators with a Bernoulli-distributed potential. The proof approximates the low eigenvalues by eigenvalues of sine waves supported where the potential takes its lower value. This is motivated by the idea that the eigenvectors associated to the low eigenvalues react to the jump in the values of the potential as if the gap were infinite.
Keywords
Cite
@article{arxiv.1403.5533,
title = {Lifschitz Tails for Random Schr\"{o}dinger Operator in Bernoulli Distributed Potentials},
author = {Michael Bishop and Vita Borovyk and Jan Wehr},
journal= {arXiv preprint arXiv:1403.5533},
year = {2015}
}