Geometrically induced discrete spectrum in curved tubes

被引：53
作者：
Chenaud, B
Duclos, P
Freitas, P
Krejcirík, D
机构：
[1] Univ Montpellier 2, Dept Math Sci, F-34095 Montpellier, France
[2] CNRS, Ctr Phys Theor, F-13288 Marseille, France
[3] Univ Toulon & Var, F-83957 La Garde, France
[4] Inst Super Tecn, Dept Matemat, P-1049001 Lisbon, Portugal
来源：
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS | 2005年 / 23卷 / 02期
关键词：
quantum waveguides; bound states; Dirichlet Laplacian; Tang frame;
D O I：
10.1016/j.difgeo.2005.05.001
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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. (c) 2005 Elsevier B.V. All rights reserved.
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页码：95 / 105
页数：11
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