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Teoreticheskaya i Matematicheskaya Fizika, 1995, Volume 103, Number 2, Pages 283–294 (Mi tmf1303)  
This article is cited in 10 scientific papers (total in 10 papers)

Spectrum of three-dimensional landau operator perturbed by a periodic point potential

V. A. Geiler, V. V. Demidov

Mordovian State University
Full-text PDF (1409 kB) Citations (10)
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Abstract: A study is made of a three-dimensional Schrödinger operator with magnetic field and perturbed by a periodic sum of zero-range potentials. In the case of a rational flux, the explicit form of the decomposition of the resolvent of this operator with respect to the spectrum of irreducible representations of the group of magnetic translations is found. In the case of integer flux, the explicit form of the dispersion laws is found, the spectrum is described, and a qualitative investigation of it is made (in particular, it is established that not more than one gap exists).
Received: 07.07.1994
English version:
Theoretical and Mathematical Physics, 1995, Volume 103, Issue 2, Pages 561–569
DOI: https://doi.org/10.1007/BF02274034
Bibliographic databases:
Language: Russian
Citation: V. A. Geiler, V. V. Demidov, “Spectrum of three-dimensional landau operator perturbed by a periodic point potential”, TMF, 103:2 (1995), 283–294; Theoret. and Math. Phys., 103:2 (1995), 561–569
Citation in format AMSBIB
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\by V.~A.~Geiler, V.~V.~Demidov
\paper Spectrum of three-dimensional landau operator perturbed by a~periodic point potential
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\pages 283--294
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\transl
\jour Theoret. and Math. Phys.
\yr 1995
\vol 103
\issue 2
\pages 561--569
\crossref{https://doi.org/10.1007/BF02274034}
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Linking options:
  • https://www.mathnet.ru/eng/tmf1303
  • https://www.mathnet.ru/eng/tmf/v103/i2/p283
    • This publication is cited in the following 10 articles:
    1. E. N. Grishanov, I. Y. Popov, “Solvable model of moire superlattice in a magnetic field”, Indian J Phys, 2024  crossref
    2. E.N. Grishanov, O.S. Gryazeva, I.Y. Popov, “Hofstadter butterflies for square and honeycomb periodic arrays of quantum dots with Aharonov-Bohm solenoids”, Micro and Nanostructures, 168 (2022), 207325  crossref
    3. E. N. Grishanov, I. Y. Popov, “Spectral Properties of Graphene with Periodic Array of Defects in a Magnetic Field”, Russ. J. Math. Phys., 25:3 (2018), 277  crossref
    4. E.N. Grishanov, I.Y. Popov, “Electron spectrum for aligned SWNT array in a magnetic field”, Superlattices and Microstructures, 100 (2016), 1276  crossref
    5. E.N. Grishanov, I.Yu. Popov, “Spectral properties of multi-layered graphene in a magnetic field”, Superlattices and Microstructures, 86 (2015), 68  crossref
    6. E. N. Grishanov, V. V. Demidov, L. A. Chernozatonskii, “Issledovanie spektralnykh svoistv sverkhreshetok nanotrubok v magnitnom pole”, Trudy chetvertoi Vserossiiskoi nauchnoi konferentsii s mezhdunarodnym uchastiem (29–31 maya 2007 g.). Chast 3, Differentsialnye uravneniya i kraevye zadachi, Matem. modelirovanie i kraev. zadachi, SamGTU, Samara, 2007, 75–78  mathnet
    7. J. Brüning, V. V. Demidov, V. A. Geyler, “Hofstadter-type spectral diagrams for the Bloch electron in three dimensions”, Phys. Rev. B, 69:3 (2004)  crossref
    8. J. BRÜNING, V. V. DEMIDOV, V. A. GEYLER, “FERMI SURFACES OF CRYSTALS IN A HIGH MAGNETIC FIELD”, Int. J. Nanosci., 02:06 (2003), 603  crossref
    9. S. Albeverio, V.A. Geyler, O.G. Kostrov, “Quasi-one-dimensional nanosystems in a uniform magnetic field: Explicitly solvable model”, Reports on Mathematical Physics, 44:1-2 (1999), 13  crossref
    10. V. A. Geyler, K. V. Pankrashkin, Mathematical Results in Quantum Mechanics, 1999, 259  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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