Publication Date:
2011-06-15
Description:
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. Content Type Journal Article Pages 606-627 DOI 10.1007/s11232-011-0046-6 Authors S. A. Nazarov, Institute of Mechanical Engineering Problems, RAS, St. Petersburg, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 2
Print ISSN:
0040-5779
Topics:
Mathematics
,
Physics
