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 TMF, 1987, Volume 70, Number 2, Pages 192–201 (Mi tmf4611)

Anderson localization in the nondiscrete maryland model

V. A. Geiler, V. A. Margulis

Abstract: The Schrödinger operator $H=H_0+V$, is considered where $V$ is an almost periodic potential of point interactions and the Hamiltonian $H_0$ is subject to certain conditions satisfied, in particular, by two- and three-dimensional operators of the form $H_0=-\Delta$ and $H_0=(i\nabla-\mathbf{A})^2$ $\mathbf{A}$ being a vector-potential of a uniform magnetic field. It is proved that under certain conditions of incommensurability for $V$, non-degenerate localised states of the operator $H$ are dense in forbidden bands of $H_0$; the expressions for corresponding eigen-functions are found.

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English version:
Theoretical and Mathematical Physics, 1987, 70:2, 133–140

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Citation: V. A. Geiler, V. A. Margulis, “Anderson localization in the nondiscrete maryland model”, TMF, 70:2 (1987), 192–201; Theoret. and Math. Phys., 70:2 (1987), 133–140

Citation in format AMSBIB
\Bibitem{GeiMar87} \by V.~A.~Geiler, V.~A.~Margulis \paper Anderson localization in the nondiscrete maryland model \jour TMF \yr 1987 \vol 70 \issue 2 \pages 192--201 \mathnet{http://mi.mathnet.ru/tmf4611} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=894466} \transl \jour Theoret. and Math. Phys. \yr 1987 \vol 70 \issue 2 \pages 133--140 \crossref{https://doi.org/10.1007/BF01039202} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1987K225600004} 

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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. 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
2. Albeverio, S, “The band structure of the general periodic Schrodinger operator with point interactions”, Communications in Mathematical Physics, 210:1 (2000), 29
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