Pavel Exner and Diana Barseghyan
Spectral estimates for Dirichlet Laplacians on perturbed twisted tubes
(182K, pdf)

ABSTRACT.  We investigate Dirichlet Laplacian in a straight twisted tube of a non-circular cross section, in particular, its discrete spectrum coming from a local slowdown of the twist. We prove a Lieb-Thirring-type estimate for the spectral moments and present two examples illustrating how the bound depends on the tube cross section.