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

作者：Nazarov S A^*

来源：Theoretical and Mathematical Physics, 2011, 167(2): 606-627.

DOI：10.1007/s11232-011-0046-6

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

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.

• 出版日期2011-5
• 单位中国地震局工程力学研究所