Low lying spectrum of weak-disorder quantum waveguides
Spectral Theory
2015-05-20 v2 Mathematical Physics
math.MP
Probability
Abstract
We study the low-lying spectrum of the Dirichlet Laplace operator on a randomly wiggled strip. More precisely, our results are formulated in terms of the eigenvalues of finite segment approximations of the infinite waveguide. Under appropriate weak-disorder assumptions we obtain deterministic and probabilistic bounds on the position of the lowest eigenvalue. A Combes-Thomas argument allows us to obtain so-called 'initial length scale decay estimates' at they are used in the proof of spectral localization using the multiscale analysis.
Cite
@article{arxiv.1010.0315,
title = {Low lying spectrum of weak-disorder quantum waveguides},
author = {Denis Borisov and Ivan Veselic'},
journal= {arXiv preprint arXiv:1010.0315},
year = {2015}
}
Comments
Accepted for publication in Journal of Statistical Physics http://www.springerlink.com/content/0022-4715