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arXiv · 1010.0315

Low lying spectrum of weak-disorder quantum waveguides

Denis Borisov·Ivan Veselic'
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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.

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Denis Borisov, Ivan Veselic'. 2010-11-24. Low lying spectrum of weak-disorder quantum waveguides. https://doi.org/10.1007/s10955-010-0099-1

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