Twisting versus bending in quantum waveguides
David Krejcirik
TL;DR
This paper reviews how twisting and bending affect the spectral properties of quantum waveguides, emphasizing Hardy inequalities in twisted tubes with non-circular cross-sections.
Contribution
It provides an overview of spectral-geometric effects and highlights the role of Hardy inequalities in twisted quantum waveguides with non-circular cross-sections.
Findings
Hardy-type inequalities are established for twisted tubes.
Spectral effects of twisting and bending are analyzed.
The impact of cross-section shape on spectral properties is discussed.
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.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Laser-Matter Interactions and Applications · Quantum optics and atomic interactions