Spectrum of the Schrödinger operator in a perturbed periodically twisted tube

Abstract

We study Dirichlet Laplacian in a screw-shaped region, i.e. a straight twisted tube of a non-circular cross section. It is shown that a local perturbation which consists of "slowing down" the twisting in the mean gives rise to a non-empty discrete spectrum.

LaTeX2e, 10 pages

References in corpus (3)

• Bound states in weakly deformed strips and layers
• Stability of the magnetic Schrödinger operator in a waveguide
• A lower bound to the spectral threshold in curved tubes

Cited by in corpus (12)

• Twisting versus bending in quantum waveguides
• Planar waveguide with "twisted" boundary conditions: discrete spectrum
• Nonadiabatic couplings and gauge-theoretical structure of curved quantum waveguides
• Quantum singular operator limits of thin Dirichlet tubes via $\Gamma$-convergence
• Spectral analysis of sheared nanoribbons
• A remark on helical waveguides
• The Hardy inequality and the heat equation in twisted tubes
• Eigenvalue and Resonance Asymptotics in perturbed periodically twisted tubes: Twisting versus Bending
• Spectral estimates for Dirichlet Laplacians on perturbed twisted tubes
• Lifshits tails for randomly twisted quantum waveguides
• Hardy inequalities in globally twisted waveguides
• Spectrum of the Dirichlet Laplacian in waveguides with parallel cross-sections