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Matematicheskie Zametki, 2013, Volume 93, Issue 2, Pages 227–245
DOI: https://doi.org/10.4213/mzm10160
(Mi mzm10160)
 

This article is cited in 10 scientific papers (total in 10 papers)

Asymptotics of an Eigenvalue on the Continuous Spectrum of Two Quantum Waveguides Coupled through Narrow Windows

S. A. Nazarovab

a Saint-Petersburg State University
b Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg
References:
Abstract: Conditions under which two planar identical waveguides coupled through narrow windows of width $\varepsilon\ll 1$ have an eigenvalue on the continuous spectrum are obtained. It is established that the eigenvalue appears only for certain values of the distance between the windows: for each sufficiently small $\varepsilon>0$, there exists a sequence $(2N-1)/\sqrt{3}+O(\varepsilon)$ of such distances; here $N=1,2,3,\dots$ . The result is obtained by the asymptotic analysis of an auxiliary object, namely, the augmented scattering matrix.
Keywords: planar waveguide, window-coupled quantum waveguides, augmented scattering matrix, Laplace operator, Dirichlet boundary condition, Neumann boundary condition, Helmholtz equation, Wood's anomalies.
Received: 10.09.2011
English version:
Mathematical Notes, 2013, Volume 93, Issue 2, Pages 266–281
DOI: https://doi.org/10.1134/S000143461301029X
Bibliographic databases:
Document Type: Article
UDC: 517.956.8:517.956.227
Language: Russian
Citation: S. A. Nazarov, “Asymptotics of an Eigenvalue on the Continuous Spectrum of Two Quantum Waveguides Coupled through Narrow Windows”, Mat. Zametki, 93:2 (2013), 227–245; Math. Notes, 93:2 (2013), 266–281
Citation in format AMSBIB
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  • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
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