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Geometrically induced discrete spectrum in curved tubes |
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| Authors: | B Chenaud P Freitas |
| Institution: | a Département des Sciences Mathématiques, Université Montpellier II, Case 051, Place Eugène Bataillon, 34 095 Montpellier cedex 5, France b Centre de Physique Théorique, CNRS, Luminy, Case 907, 13 288 Marseille cedex 9, France c PhyMat, Université de Toulon et du Var, BP 132, 83 957 La Garde, France d Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal |
| Abstract: | The Dirichlet Laplacian in curved tubes of arbitrary cross-section rotating w.r.t. the Tang frame along infinite curves in Euclidean spaces of arbitrary dimension is investigated. If the reference curve is not straight and its curvatures vanish at infinity, we prove that the essential spectrum as a set coincides with the spectrum of the straight tube of the same cross-section and that the discrete spectrum is not empty. |
| Keywords: | 81Q10 58J50 53A04 |
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