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

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Abstract

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.

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Authors and Affiliations

  1. Institute of Mechanical Engineering Problems, RAS, St. Petersburg, Russia

    S. A. Nazarov

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  1. S. A. Nazarov
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Correspondence to S. A. Nazarov.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 167, No. 2, pp. 239–263, May, 2011.

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Nazarov, S.A. Asymptotic expansions of eigenvalues in the continuous spectrum of a regularly perturbed quantum waveguide. Theor Math Phys 167, 606–627 (2011). https://doi.org/10.1007/s11232-011-0046-6

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