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

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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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
\Bibitem{GeiMar84} \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
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
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
4. L. I. Danilov, “O spektre dvumernogo operatora Shredingera s odnorodnym magnitnym polem i periodicheskim elektricheskim potentsialom”, Izv. IMI UdGU, 51 (2018), 3–41
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