RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Zametki, 2013, Volume 93, Issue 2, Pages 227–245 (Mi mz10160)  

This article is cited in 6 scientific papers (total in 6 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

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 $N=1,2,3,…$ . 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.

DOI: https://doi.org/10.4213/mzm10160

Full text: PDF file (646 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2013, 93:2, 266–281

Bibliographic databases:

UDC: 517.956.8:517.956.227
Received: 10.09.2011

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
\Bibitem{Naz13}
\by S.~A.~Nazarov
\paper Asymptotics of an Eigenvalue on the Continuous Spectrum of Two Quantum Waveguides Coupled through Narrow Windows
\jour Mat. Zametki
\yr 2013
\vol 93
\issue 2
\pages 227--245
\mathnet{http://mi.mathnet.ru/mz10160}
\crossref{https://doi.org/10.4213/mzm10160}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3205969}
\zmath{https://zbmath.org/?q=an:06158184}
\elib{http://elibrary.ru/item.asp?id=20731678}
\transl
\jour Math. Notes
\yr 2013
\vol 93
\issue 2
\pages 266--281
\crossref{https://doi.org/10.1134/S000143461301029X}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000315582900029}
\elib{http://elibrary.ru/item.asp?id=20431949}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84874572143}


Linking options:
  • http://mi.mathnet.ru/eng/mz10160
  • https://doi.org/10.4213/mzm10160
  • http://mi.mathnet.ru/eng/mz/v93/i2/p227

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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, “Almost standing waves in a periodic waveguide with a resonator and near-threshold eigenvalues”, St. Petersburg Math. J., 28:3 (2017), 377–410  mathnet  crossref  mathscinet  isi  elib
    2. A. R. Bikmetov, R. R. Gadyl'shin, “On local perturbations of waveguides”, Russ. J. Math. Phys., 23:1 (2016), 1–18  crossref  mathscinet  zmath  isi  scopus
    3. T. Durante, “Waveguides with a box-shaped perturbation: eigenvalues of the Neumann problem”, Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2016 (ICNAAM-2016), AIP Conf. Proc., 1863, eds. T. Simos, C. Tsitouras, Amer Inst Physics, 2017, UNSP 510003-1  crossref  isi
    4. A. Haenel, T. Weidl, “Spectral asymptotics for the Dirichlet Laplacian with a Neumann window via a Birman-Schwinger analysis of the Dirichlet-to-Neumann operator”, Functional Analysis and Operator Theory For Quantum Physics: the Pavel Exner Anniversary Volume, EMS Ser. Congr. Rep., eds. Dittrich J., Kovarik H., Laptev A., Eur. Math. Soc., 2017, 315–352  mathscinet  zmath  isi
    5. G. Cardone, T. Durante, S. A. Nazarov, “Embedded eigenvalues of the Neumann problem in a strip with a box-shaped perturbation”, J. Math. Pures Appl., 112 (2018), 1–40  crossref  mathscinet  zmath  isi
    6. S. A. Nazarov, “Transmission of waves through a small aperture in the cross-wall in an acoustic waveguide”, Siberian Math. J., 59:1 (2018), 85–101  mathnet  crossref  crossref  isi  elib
  • Математические заметки Mathematical Notes
    Number of views:
    This page:438
    Full text:49
    References:61
    First page:36

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019