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Mat. Zametki, 2007, Volume 81, Issue 1, Pages 32–42 (Mi mz3515)  

This article is cited in 2 scientific papers (total in 2 papers)

Quantization of Periodic Motions on Compact Surfaces of Constant Negative Curvature in a Magnetic Field

J. Brüninga, R. V. Nekrasova, A. I. Shafarevichb

a M. V. Lomonosov Moscow State University
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We use the semiclassical approach to study the spectral problem for the Schrödinger operator of a charged particle confined to a two-dimensional compact surface of constant negative curvature. We classify modes of classical motion in the integrable domain $E<E_{cr}$ and obtain a classification of semiclassical solutions as a consequence. We construct a spectral series (spectrum part approximated by semiclassical eigenvalues) corresponding to energies not exceeding the threshold value $E_{cr}$; the degeneration multiplicity is computed for each eigenvalue.

Keywords: Schrödinger equation, eigenvalue asymptotics, semiclassical approximation, confined classical motion, surface of negative curvature, symplectic structure

DOI: https://doi.org/10.4213/mzm3515

Full text: PDF file (510 kB)
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English version:
Mathematical Notes, 2007, 81:1, 28–36

Bibliographic databases:

UDC: 517.958+530.145.6
Received: 17.05.2006
Revised: 28.06.2006

Citation: J. Brüning, R. V. Nekrasov, A. I. Shafarevich, “Quantization of Periodic Motions on Compact Surfaces of Constant Negative Curvature in a Magnetic Field”, Mat. Zametki, 81:1 (2007), 32–42; Math. Notes, 81:1 (2007), 28–36

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Brüning J., Dobrokhotov S. Yu., Nekrasov R. V., “Quantum dynamics in a thin film. II. Stationary states”, Russ. J. Math. Phys., 16:4 (2009), 467–477  crossref  mathscinet  zmath  isi  elib  scopus
    2. Yu. A. Kordyukov, I. A. Taimanov, “Trace formula for the magnetic Laplacian”, Russian Math. Surveys, 74:2 (2019), 325–361  mathnet  crossref  crossref  adsnasa  isi  elib
  • Математические заметки Mathematical Notes
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