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Zh. Vychisl. Mat. Mat. Fiz., 2018, Volume 58, Number 11, Pages 1911–1931 (Mi zvmmf10847)  

This article is cited in 4 scientific papers (total in 4 papers)

Various manifestations of Wood anomalies in locally distorted quantum waveguides

S. A. Nazarov

St. Petersburg State University, St. Petersburg, Russia

Abstract: Anomalies of the diffraction pattern at near-threshold frequencies of the continuous spectrum of a cylindrical quantum waveguide with regular (smooth gentle) or singular (small cavities and bumps) perturbations of the boundary are studied. Wood anomalies are characterized by rapid variations in the scattering matrix near the thresholds. Conditions under which a Wood anomaly is absent, appears, and enhances are obtained by constructing asymptotics of solutions to the Dirichlet problem for the Helmholtz equation. The results are obtained by analyzing an artificial object — the augmented scattering matrix — and involve only operations with real values of the spectral parameter, but the relation between Wood anomalies and complex resonance points is also considered. Generated by almost standing waves, threshold resonances that cause near-threshold anomalies of other types are discussed.

Key words: quantum waveguide, regular and singular perturbations of the boundary, asymptotics, resonances, near-threshold frequencies, Wood anomaly.

Funding Agency Grant Number
Russian Science Foundation 17-11-01003


DOI: https://doi.org/10.31857/S004446690003542-7

References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2018, 58:11, 1838–1855

Bibliographic databases:

UDC: 517.956.8:517.958
Received: 24.10.2017

Citation: S. A. Nazarov, “Various manifestations of Wood anomalies in locally distorted quantum waveguides”, Zh. Vychisl. Mat. Mat. Fiz., 58:11 (2018), 1911–1931; Comput. Math. Math. Phys., 58:11 (2018), 1838–1855

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. A. Nazarov, “Waveguide with double threshold resonance at a simple threshold”, Sb. Math., 211:8 (2020), 1080–1126  mathnet  crossref  crossref  mathscinet  isi  elib
    2. S. A. Nazarov, “Threshold resonances and virtual levels in the spectrum of cylindrical and periodic waveguides”, Izv. Math., 84:6 (2020), 1105–1160  mathnet  crossref  crossref  mathscinet  isi  elib
    3. F. L. Bakharev, S. A. Nazarov, “Kriterii otsutstviya i nalichiya ogranichennykh reshenii na poroge nepreryvnogo spektra v ob'edinenii kvantovykh volnovodov”, Algebra i analiz, 32:6 (2020), 1–23  mathnet
    4. S. A. Nazarov, K. M. Ruotsalainen, P. I. Uusitalo, “Koeffitsienty rasseyaniya i porogovye rezonansy v volnovode pri ravnomernom rastyazhenii rezonatora”, Matematicheskie voprosy teorii rasprostraneniya voln. 51, Zap. nauchn. sem. POMI, 506, POMI, SPb., 2021, 175–209  mathnet
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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