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TMF, 1984, Volume 61, Number 1, Pages 140–149 (Mi tmf5668)  

This article is cited in 4 scientific papers (total in 4 papers)

Structure of the spectrum of a bloch electron in a magnetic field in a two-dimensional lattice

V. A. Geiler, V. A. Margulis


Abstract: A study is made of the Hamiltonian H of an electron in a two-dimensional lattice of point potentials in a transverse magnetic field whose flux is rational. An expansion of H in a direct integral over a two-dimensional torus of the reciprocal lattice of operators described by finite-dimensional matrices is obtained. This expansion is used to investigate the structure of the spectrum of H, whose continuum eigenfunctions are found.

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English version:
Theoretical and Mathematical Physics, 1984, 61:1, 1049–1056

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Received: 02.11.1983

Citation: V. A. Geiler, V. A. Margulis, “Structure of the spectrum of a bloch electron in a magnetic field in a two-dimensional lattice”, TMF, 61:1 (1984), 140–149; Theoret. and Math. Phys., 61:1 (1984), 1049–1056

Citation in format AMSBIB
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\by V.~A.~Geiler, V.~A.~Margulis
\paper Structure of the spectrum of a bloch electron in a magnetic field in a two-dimensional lattice
\jour TMF
\yr 1984
\vol 61
\issue 1
\pages 140--149
\mathnet{http://mi.mathnet.ru/tmf5668}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=774214}
\transl
\jour Theoret. and Math. Phys.
\yr 1984
\vol 61
\issue 1
\pages 1049--1056
\crossref{https://doi.org/10.1007/BF01038554}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1984AGK6100013}


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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. V. A. Geiler, V. A. Margulis, “Anderson localization in the nondiscrete maryland model”, Theoret. and Math. Phys., 70:2 (1987), 133–140  mathnet  crossref  mathscinet  isi
    2. V. A. Geiler, V. V. Demidov, “Spectrum of three-dimensional landau operator perturbed by a periodic point potential”, Theoret. and Math. Phys., 103:2 (1995), 561–569  mathnet  crossref  mathscinet  zmath  isi
    3. V. A. Geiler, V. A. Margulis, “Point perturbation-invariant solutions of the Schrödinger equation with a magnetic field”, Math. Notes, 60:5 (1996), 575–580  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. L. I. Danilov, “O spektre dvumernogo operatora Shredingera s odnorodnym magnitnym polem i periodicheskim elektricheskim potentsialom”, Izv. IMI UdGU, 51 (2018), 3–41  mathnet  crossref  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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