We consider the Harper equation ψ(x + h) + ψ(x - h) + 2λ cos (2πx)ψ(x) = Eψ(x), x R, where h > 0, 0 < λ ≤ 1, and E ϵ R are parameters. This equation appears as a model in solid state physics and has intriguing spectral properties. In the quasiclassical limit, i.e., as h → 0, we describe the asymptotics of monodromy matrices for the Harper equation. This enables us to get information on the asymptotic structure of the spectrum.

Original languageEnglish
Title of host publicationProceedings of the International Conference Days on Diffraction, DD 2018
EditorsA.Ya. Kazakov, A.P. Kiselev, L.I. Goray, O.V. Motygin
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages4
ISBN (Print)978-1-7281-0313-6
Publication statusPublished - 2018
EventInternational conference Days on Diffraction-2018 - St Petersburg
Duration: 4 Jun 20188 Jun 2018


ConferenceInternational Conference on Days on Diffraction (DD)
CountryRussian Federation
CitySt Petersburg

Scopus subject areas

  • Mechanics of Materials
  • Safety, Risk, Reliability and Quality
  • Computational Mathematics
  • Astronomy and Astrophysics
  • Radiation

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    Fedotov, A., & Shchetka, E. (2018). Monodromy matrices for Harper equation. In A. Y. Kazakov, A. P. Kiselev, L. I. Goray, & O. V. Motygin (Eds.), Proceedings of the International Conference Days on Diffraction, DD 2018 (pp. 102-105). [8553420] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/DD.2018.8553420