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TMF, 1980, Volume 45, Number 2, Pages 268–275 (Mi tmf3889)  

This article is cited in 7 scientific papers (total in 7 papers)

Peierls-Fröhlich problem and potentials with finite number of gaps. I

E. D. Belokolos


Abstract: Exact solution of the Peierls–Fröhlich problem about the self-consistent state of conduction electron and lattice is proved to be a one-gap potential. Equations which describe the dependence of the boundaries of the spectrum on the parameters of the problem (such as the electron density, lattice elastic constant and temperature) are obtained. The equations are exactly solved at the absolute zero of temperature and investigated at the critical temperature at which lattice deformations arise. Charge density waves and condensons are shown to be limiting cases of the considered selfconsistent state.

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English version:
Theoretical and Mathematical Physics, 1980, 45:2, 1022–1026

Bibliographic databases:

Received: 21.04.1980

Citation: E. D. Belokolos, “Peierls-Fröhlich problem and potentials with finite number of gaps. I”, TMF, 45:2 (1980), 268–275; Theoret. and Math. Phys., 45:2 (1980), 1022–1026

Citation in format AMSBIB
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\by E.~D.~Belokolos
\paper Peierls-Fr\"ohlich problem and potentials with finite number of~gaps.~I
\jour TMF
\yr 1980
\vol 45
\issue 2
\pages 268--275
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=604525}
\transl
\jour Theoret. and Math. Phys.
\yr 1980
\vol 45
\issue 2
\pages 1022--1026
\crossref{https://doi.org/10.1007/BF01028601}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1980LZ19000012}


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  • http://mi.mathnet.ru/eng/tmf/v45/i2/p268

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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. E. D. Belokolos, “Peierls-Fröhlich problem and potentials with finite number of gaps. II”, Theoret. and Math. Phys., 48:1 (1981), 604–610  mathnet  crossref  mathscinet  isi
    2. I. M. Krichever, “The Peierls model”, Funct. Anal. Appl., 16:4 (1982), 248–263  mathnet  crossref  mathscinet  isi
    3. E. D. Belokolos, I. M. Pershko, “Classification of quasione-dimensional Peierls–Frehlich conductors”, Theoret. and Math. Phys., 58:2 (1984), 183–191  mathnet  crossref  isi
    4. E. D. Belokolos, D. Ya. Petrina, “Connection between the approximating Hamiltonian method and theta-function integration”, Theoret. and Math. Phys., 58:1 (1984), 40–46  mathnet  crossref  mathscinet  isi
    5. A. A. Dzhalilov, V. A. Chulaevskii, “Thermodynamic properties of the Peierls model”, Theoret. and Math. Phys., 63:3 (1985), 630–634  mathnet  crossref  mathscinet  isi
    6. E. D. Belokolos, A. I. Bobenko, V. B. Matveev, V. Z. Ènol'skii, “Algebraic-geometric principles of superposition of finite-zone solutions of integrable non-linear equations”, Russian Math. Surveys, 41:2 (1986), 1–49  mathnet  crossref  mathscinet  zmath  isi
    7. I. M. Krichever, “Spectral theory of finite-zone nonstationary Schrödinger operators. A nonstationary Peierls model”, Funct. Anal. Appl., 20:3 (1986), 203–214  mathnet  crossref  mathscinet  zmath  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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