Asymptotic expansions of eigenvalues in the continuous spectrum of a regularly perturbed quantum waveguide

被引：0

作者：

S. A. Nazarov

机构：

[1] RAS,Institute of Mechanical Engineering Problems

来源：

Theoretical and Mathematical Physics | 2011年 / 167卷

关键词：

quantum waveguide; regular perturbation of the boundary; asymptotic expansion of eigenvalue on the continuous spectrum; Wood’s anomalies;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We establish that by choosing a smooth local perturbation of the boundary of a planar quantum waveguide, we can create an eigenvalue near any given threshold of the continuous spectrum and the corresponding trapped wave exponentially decaying at infinity. Based on an analysis of an auxiliary object, a unitary augmented scattering matrix, we asymptotically interpret Wood’s anomalies, the phenomenon of fast variations in the diffraction pattern due to variations in the near-threshold wave frequency.

引用

页码：606 / 627

页数：21

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