Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4590646 | Journal of Functional Analysis | 2013 | 33 Pages |
Abstract
We consider the negative Dirichlet Laplacian on an infinite waveguide embedded in R2R2, 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Denis Borisov, Ivan Veselić,