Low lying eigenvalues of randomly curved quantum waveguides
arXiv:1211.1314 · doi:10.1016/j.jfa.2013.08.011
Abstract
We consider the negative Dirichlet Laplacian on an infinite waveguide embedded in $\RR^2$, and finite segments thereof. The waveguide is a perturbation of a periodic strip in terms of a sequence of independent identically distributed random variables which influence the curvature. We derive explicit lower bounds on the first eigenvalue of finite segments of the randomly curved waveguide in the small coupling (i.e. weak disorder) regime. This allows us to estimate the probability of low lying eigenvalues, a tool which is relevant in the context of Anderson localization for random Schrödinger operators.
Minor changes to first version, accepted for publication in: Journal of Functional Analysis
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- Lifshits tails for randomly twisted quantum waveguides
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- Lifshitz asymptotics and localization for random breather models