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TMF, 1981, Volume 48, Number 1, Pages 60–69 (Mi tmf4472)  

This article is cited in 5 scientific papers (total in 5 papers)

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

E. D. Belokolos


Abstract: A generalized Peierls–Fröhlich problem on the formation of a forbidden band in the energy spectrum of electrons due to the deformation of a potential which originally has $n$ bands is formulated. It is shown that the solutions to this problem, which are the extremals of the generalized functional of the Peierls–Fröhlich free energy, form a $(n+1)$-parameter manifold of $(n+1)$-gap potentials. Equations are obtained which the boundaries of the gaps of these potentials satisfy. It is shown that the motions on the manifold of solutions of the considered problem described by Korteweg–de Vries equations are Fröhlieh collective modes. The theory makes it possible to describe phase transitions of a lattice between periodic and quasiperiodie structures.

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English version:
Theoretical and Mathematical Physics, 1981, 48:1, 604–610

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Received: 09.06.1980

Citation: E. D. Belokolos, “Peierls-Fröhlich problem and potentials with finite number of gaps. II”, TMF, 48:1 (1981), 60–69; Theoret. and Math. Phys., 48:1 (1981), 604–610

Citation in format AMSBIB
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\by E.~D.~Belokolos
\paper Peierls-Fr\"ohlich problem and potentials with finite number of gaps.~II
\jour TMF
\yr 1981
\vol 48
\issue 1
\pages 60--69
\mathnet{http://mi.mathnet.ru/tmf4472}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=630270}
\transl
\jour Theoret. and Math. Phys.
\yr 1981
\vol 48
\issue 1
\pages 604--610
\crossref{https://doi.org/10.1007/BF01037985}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1981ND61200007}


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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. I. M. Krichever, “The Peierls model”, Funct. Anal. Appl., 16:4 (1982), 248–263  mathnet  crossref  mathscinet  isi
    2. 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
    3. 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
    4. 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
    5. 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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