CURVATURE-INDUCED BOUND STATES IN QUANTUM WAVEGUIDES IN TWO AND THREE DIMENSIONS
CURVATURE-INDUCED BOUND STATES IN QUANTUM WAVEGUIDES IN TWO AND THREE DIMENSIONS
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二维和三维量子波导中曲率引起的束缚态
DOI：
10.1142/s0129055x95000062
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发表时间：
1995
影响因子：
1.8
通讯作者：
P. Exner
中科院分区：
文献类型：
--
作者：
P. Duclos;P. Exner
研究了二维和三维等截面弯曲管上的狄利克雷拉普拉斯算子。证明了如果管是非直的且曲率渐近消失，则在基本谱的底部以下总存在一个束缚态。导出了细管中这些束缚态数目的上限。此外，如果管子只是轻微弯曲，则只有一个束缚态；我们推导出它关于弯曲角的特性。最后，构造了这些特征值在任意细管中对管半径的摄动理论，并提出了一些开放问题。
Dirichlet Laplacian on curved tubes of a constant cross section in two and three dimensions is investigated. It is shown that if the tube is non-straight and its curvature vanishes asymptotically, there is always a bound state below the bottom of the essential spectrum. An upper bound to the number of these bound states in thin tubes is derived. Furthermore, if the tube is only slightly bent, there is just one bound state; we derive its behaviour with respect to the bending angle. Finally, perturbation theory of these eigenvalues in any thin tube with respect to the tube radius is constructed and some open questions are formulated.