Abstract:
The Schrödinger operator H=H0+V, is considered where V is an almost periodic potential of point interactions and the Hamiltonian H0 is subject to certain conditions satisfied, in particular, by two- and three-dimensional operators of the form H0=−Δ and H0=(i∇−A)2A 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 H0; the expressions for corresponding eigen-functions are found.
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
\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://mathscinet.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{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1987K225600004}
Linking options:
https://www.mathnet.ru/eng/tmf4611
https://www.mathnet.ru/eng/tmf/v70/i2/p192
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Albeverio, S, “The band structure of the general periodic Schrodinger operator with point interactions”, Communications in Mathematical Physics, 210:1 (2000), 29
S.A. Gredeskul, M. Zusman, Y. Avishai, M.Ya. Azbel', “Spectral properties and localization of an electron in a two-dimensional system with point scatterers in a magnetic field”, Physics Reports, 288:1-6 (1997), 223
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
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