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TMF, 2002, Volume 131, Number 2, Pages 304–331 (Mi tmf332)  

This article is cited in 5 scientific papers (total in 5 papers)

The Asymptotic Form of the Lower Landau Bands in a Strong Magnetic Field

J. Brüninga, S. Yu. Dobrokhotovb, K. V. Pankrashinba

a Humboldt University
b A. Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences

Abstract: The asymptotic form of the bottom part of the spectrum of the two-dimensional magnetic Schrödinger operator with a periodic potential in a strong magnetic field is studied in the semiclassical approximation. Averaging methods permit reducing the corresponding classical problem to a one-dimensional problem on the torus; we thus show the almost integrability of the original problem. Using elementary corollaries from the topological theory of Hamiltonian systems, we classify the almost invariant manifolds of the classical Hamiltonian. The manifolds corresponding to the bottom part of the spectrum are closed or nonclosed curves and points. Their geometric and topological characteristics determine the asymptotic form of parts of the spectrum (spectral series). We construct this asymptotic form using the methods of the semiclassical approximation with complex phases. We discuss the relation of the asymptotic form obtained to the magneto-Bloch conditions and asymptotics of the band spectrum.

DOI: https://doi.org/10.4213/tmf332

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English version:
Theoretical and Mathematical Physics, 2002, 131:2, 704–728

Bibliographic databases:

Received: 14.01.2002

Citation: J. Brüning, S. Yu. Dobrokhotov, K. V. Pankrashin, “The Asymptotic Form of the Lower Landau Bands in a Strong Magnetic Field”, TMF, 131:2 (2002), 304–331; Theoret. and Math. Phys., 131:2 (2002), 704–728

Citation in format AMSBIB
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\paper The Asymptotic Form of the Lower Landau Bands in a Strong Magnetic Field
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\yr 2002
\vol 131
\issue 2
\pages 304--331
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\crossref{https://doi.org/10.4213/tmf332}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1932256}
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\transl
\jour Theoret. and Math. Phys.
\yr 2002
\vol 131
\issue 2
\pages 704--728
\crossref{https://doi.org/10.1023/A:1015433000783}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Bruning, J, “The spectral asymptotics of the two-dimensional Schrodinger operator with a strong magnetic field. II”, Russian Journal of Mathematical Physics, 9:4 (2002), 400  crossref  mathscinet  zmath  isi  scopus
    2. J. Brüning, S. Yu. Dobrokhotov, V. A. Geiler, K. Pankrashkin, “Hall conductivity of minibands lying at the wings of Landau levels”, JETP Letters, 77:11 (2003), 616–618  mathnet  crossref
    3. Pankrashkin K, “On semiclassical dispersion relations of Harper-like operators”, Journal of Physics A-Mathematical and General, 37:48 (2004), 11681–11698  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    4. A. Yu. Anikin, J. Brüning, S. Yu. Dobrokhotov, “Averaging and trajectories of a Hamiltonian system appearing in graphene placed in a strong magnetic field and a periodic potential”, J. Math. Sci., 223:6 (2017), 656–666  mathnet  crossref  mathscinet  elib
    5. Yu. A. Kordyukov, I. A. Taimanov, “Kvaziklassicheskoe priblizhenie dlya magnitnykh monopolei”, UMN, 75:6(456) (2020), 85–106  mathnet  crossref
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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