Denis Borisov, Ivan Veselić: Low lying eigenvalues of randomly curved quantum waveguides

Author(s):

Denis Borisov
Ivan Veselić

Title:

Denis Borisov, Ivan Veselić: Low lying eigenvalues of randomly curved quantum waveguides

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 11, 2013

Mathematics Subject Classification:

35P15	[]
35C20	[]
60H25	[]
82B44	[]

Abstract:

We consider the negative Dirichlet Laplacian on an infinite waveguide embedded in ℝ², 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.

Keywords:

Language:

English

Publication time:

06/2013