Low lying spectrum of weak-disorder quantum waveguides

Details Low lying spectrum of weak-disorder quantum waveguides Low lying spectrum of weak-disorder quantum waveguides

2010-10-02

arxiv.org/abs/1010.0315v2

Mathematics

Spectral Theory

Accepted for publication in Journal of Statistical Physics http://www.springerlink.com/content/0022-4715

Scientific paper

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.

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