Dislocation problem for the Dirac operator

Evgeny L. Korotyaev, Дмитрий Сергеевич Мокеев

Research outputpeer-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
Publication statusPublished - Jun 2019
Event2019 International Conference on Days on Diffraction, DD 2019 - St. Petersburg
Duration: 3 Jun 20197 Jun 2019

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

Scopus subject areas

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

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  • Cite this

    Korotyaev, E. L., & Мокеев, Д. С. (2019). Dislocation problem for the Dirac operator. In O. V. Motygin, A. P. Kiselev, L. I. Goray, A. A. Fedotov, A. Y. Kazakov, & A. S. Kirpichnikova (Eds.), Proceedings of the International Conference on Days on Diffraction 2019, DD 2019 (pp. 94-98). [9016424] (Proceedings of the International Conference on Days on Diffraction 2019, DD 2019). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/DD46733.2019.9016424