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Sbornik: Mathematics, 1998, Volume 189, Issue 6, Pages 901–930
DOI: https://doi.org/10.1070/sm1998v189n06ABEH000325
(Mi sm325)
 

This article is cited in 8 scientific papers (total in 9 papers)

Quasi-classical asymptotics of quasi-particles

V. P. Maslov, A. S. Mishchenko

M. V. Lomonosov Moscow State University
References:
Abstract: The $n$-particle problem of the Schrodinger–Laplace–Beltrami equation on a manifold with an arbitrary interaction potential between particles is studied. A pseudodifferential operator $(\operatorname {mod}h^\infty )$ on the manifold is obtained that describes the energy level of the Hamiltonian for a self-consistent field. The equations for a quasi-particle are the variational equations for the non-linear Wigner equation corresponding to the Hartree equation. Expressions are obtained for both the asymptotics of the steady-state Wigner–Hartree equation corresponding to an energy level in the ergodic situation, and the asymptotics of a generalized eigenfunction of the variational equation corresponding to the same energy level manifold. The asymptotic recursion relations for the indicated problem in the case studied by Bogolyubov reduce to his results.
Received: 18.04.1997
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: Primary 81S30, 81Q20; Secondary 35S10, 82D50, 35P20, 81U30
Language: English
Original paper language: Russian
Citation: V. P. Maslov, A. S. Mishchenko, “Quasi-classical asymptotics of quasi-particles”, Sb. Math., 189:6 (1998), 901–930
Citation in format AMSBIB
\Bibitem{MasMis98}
\by V.~P.~Maslov, A.~S.~Mishchenko
\paper Quasi-classical asymptotics of quasi-particles
\jour Sb. Math.
\yr 1998
\vol 189
\issue 6
\pages 901--930
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\crossref{https://doi.org/10.1070/sm1998v189n06ABEH000325}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1657360}
\zmath{https://zbmath.org/?q=an:0920.58048}
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Linking options:
  • https://www.mathnet.ru/eng/sm325
  • https://doi.org/10.1070/sm1998v189n06ABEH000325
  • https://www.mathnet.ru/eng/sm/v189/i6/p85
  • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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