Twisting versus bending in quantum waveguides
arXiv:0712.3371
Abstract
We make an overview of spectral-geometric effects of twisting and bending in quantum waveguides modelled by the Dirichlet Laplacian in an unbounded three-dimensional tube of uniform cross-section. We focus on the existence of Hardy-type inequalities in twisted tubes of non-circular cross-section.
20 pages, LaTeX with 3 EPS figures. This is a corrected version of the published paper; errata in Section 6 corrected
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Cited by in corpus (11)
- Location of the essential spectrum in curved quantum layers
- Effective Hamiltonians for Constrained Quantum Systems
- Effective Hamiltonians for Thin Dirichlet Tubes with Varying Cross-Section
- On the spectrum and weakly effective operator for Dirichlet Laplacian in thin deformed tubes
- The NLS limit for bosons in a quantum waveguide
- Quantum strips in higher dimensions
- The Hardy inequality and the heat equation with magnetic field in any dimension
- The Hardy inequality and the heat equation in twisted tubes
- Hardy inequalities in globally twisted waveguides
- Schrödinger operator in the limit of shrinking wave-guide cross section and singularity scaled twisting
- Eigenvalue Asymptotics of Narrow Domains