Dislocation problem for the Dirac operator

Evgeny L. Korotyaev, Dmitrii S. Mokeev

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

Abstract

We consider the dislocation problem for the Dirac operator with a periodic potential on the real line. The dislocation is parameterized by a real parameter. For each parameter value, the absolutely continuous spectrum has a band structure and there are open gaps between spectral bands. We show that in each open gap there exist exactly two distinct 'states' (eigenvalues or resonances) of the dislocated operator, such that they runs clockwise around the gap. These states are separated from each other by the Dirichlet eigenvalue and they make half as many revolutions as the Dirichlet eigenvalue does in unit time. We find asymptotic of this motion for the cases when a state is near the gaps boundary and collides with the Dirichlet eigenvalue.

Original languageEnglish
Title of host publicationProceedings of the International Conference on Days on Diffraction 2019, DD 2019
EditorsOleg V. Motygin, Aleksei P. Kiselev, Leonid I. Goray, A.A. Fedotov, A.Ya. Kazakov, Anna S. Kirpichnikova
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages94-98
Number of pages5
ISBN (Electronic)9781728158372
DOIs
StatePublished - Jun 2019
Event2019 International Conference on Days on Diffraction, DD 2019 - ПОМИ РАН, St. Petersburg, Russian Federation
Duration: 3 Jun 20197 Jun 2019
http://www.pdmi.ras.ru/~dd/download/DD19_program.pdf

Publication series

NameProceedings of the International Conference on Days on Diffraction 2019, DD 2019

Conference

Conference2019 International Conference on Days on Diffraction, DD 2019
CountryRussian Federation
CitySt. Petersburg
Period3/06/197/06/19
Internet address

Scopus subject areas

  • Computational Mathematics
  • Mathematical Physics
  • Acoustics and Ultrasonics
  • Atomic and Molecular Physics, and Optics
  • Radiation

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