Lieb-Thirring inequalities for geometrically induced bound states

Abstract

We prove new inequalities of the Lieb-Thirring type on the eigenvalues of Schrödinger operators in wave guides with local perturbations. The estimates are optimal in the weak-coupling case. To illustrate their applications, we consider, in particular, a straight strip and a straight circular tube with either mixed boundary conditions or boundary deformations.

LaTeX2e, 14 pages

References in corpus (1)

• Geometric coupling thresholds in a two-dimensional strip

Cited by in corpus (6)

• Geometrically induced two-particle binding in a wave guide
• Semiclassical bounds in magnetic bottles
• Improved Berezin-Li-Yau inequalities with magnetic field
• Spectral estimates for Dirichlet Laplacians and Schroedinger operators on geometrically nontrivial cusps
• Estimates on trapped modes in deformed quantum layers
• Spectral estimates for Dirichlet Laplacians on perturbed twisted tubes