Spectrum of Laplacians on periodic graphs with guides

E. Korotyaev, Наталья Сабурова

Research outputpeer-review

Abstract

We consider Laplace operators on periodic discrete graphs perturbed by guides, i.e., graphs which are periodic in some directions and finite in other ones. We show that the spectrum of the Laplacian on the perturbed graph consists of the spectrum of the Laplacian on the unperturbed periodic graph and the additional so-called guided spectrum which is a union of a finite number of bands. We estimate the position of the guided bands and their length in terms of geometric parameters of the graph. We also determine the asymptotics of the guided bands for guides with large multiplicity of edges.

Original languageEnglish
Title of host publicationProceedings of the International Conference Days on Diffraction 2017, DD 2017
EditorsA.P. Kiselev, A.Ya. Kazakov, O.V. Motygin, L.I. Goray, T.A. Suslina, A.S. Kirpichnikova
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages282-287
Number of pages6
Volume2017-December
ISBN (Electronic)9781538647967
DOIs
Publication statusPublished - 5 Dec 2017
Event2017 International Conference Days on Diffraction, DD 2017 - St. Petersburg
Duration: 18 Jun 201722 Jun 2017

Conference

Conference2017 International Conference Days on Diffraction, DD 2017
CountryRussian Federation
CitySt. Petersburg
Period18/06/1722/06/17

Scopus subject areas

  • Acoustics and Ultrasonics
  • Surfaces and Interfaces
  • Radiation
  • Electronic, Optical and Magnetic Materials
  • Electrical and Electronic Engineering

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    Korotyaev, E., & Сабурова, Н. (2017). Spectrum of Laplacians on periodic graphs with guides. In A. P. Kiselev, A. Y. Kazakov, O. V. Motygin, L. I. Goray, T. A. Suslina, & A. S. Kirpichnikova (Eds.), Proceedings of the International Conference Days on Diffraction 2017, DD 2017 (Vol. 2017-December, pp. 282-287). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/DD.2017.8168040