The nature of the essential spectrum in curved quantum waveguides

DOI10.1088/0305-4470/37/20/013zbMath1062.81046arXivmath-ph/0307019OpenAlexW3102224055MaRDI QIDQ3158667

Rafael Tiedra de Aldecoa, David Krejčiřík

Publication date: 31 January 2005

Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0307019

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Applications of operator theory in the physical sciences (47N50) General theory of partial differential operators (47F05) PDEs in connection with quantum mechanics (35Q40) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10)

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QUANTUM COLLISIONS IN SEMI-CONSTRAINED STRUCTURES ⋮ Mathematical scattering theory in quantum and acoustic waveguides ⋮ Scattering properties for a pair of Schrödinger type operators on cylindrical domains ⋮ Existence of bound states for layers built over hypersurfaces in \(\mathbb R^{n+1}\) ⋮ Strong coupling asymptotics for Schrödinger operators with an interaction supported by an open arc in three dimensions ⋮ Scattering in twisted waveguides ⋮ SPECTRAL ANALYSIS AND TIME-DEPENDENT SCATTERING THEORY ON MANIFOLDS WITH ASYMPTOTICALLY CYLINDRICAL ENDS ⋮ On the essential spectrum of quantum waveguides ⋮ Spectrum of the Dirichlet Laplacian in sheared waveguides ⋮ Ruled strips with asymptotically diverging twisting ⋮ Absolute continuity of the spectrum in a twisted Dirichlet-Neumann waveguide ⋮ Geometrically induced discrete spectrum in curved tubes ⋮ Dirichlet Laplacian in a thin twisted strip ⋮ On the spectrum of curved planar waveguides ⋮ Schrödinger operator with decreasing potential in a cylinder

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