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TMF, 1984, Volume 61, Number 1, Pages 118–127 (Mi tmf5664)  

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

Asymptotic behavior of the spectrum of mixed states for self-consistent field equations

M. V. Karasev


Abstract: Classical and quantum action-angle variables are determined for the self-consistent Vlasov equations. Examples of their calculation are given. A reduction of the Vlasov equation with respect to a noncommuting set of first integrals that is closed with respect to the Poisson brackets is constructed. A scheme of semiclassical quantization of the reduced equation is outlined.

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English version:
Theoretical and Mathematical Physics, 1984, 61:1, 1034–1040

Bibliographic databases:

Received: 17.06.1983

Citation: M. V. Karasev, “Asymptotic behavior of the spectrum of mixed states for self-consistent field equations”, TMF, 61:1 (1984), 118–127; Theoret. and Math. Phys., 61:1 (1984), 1034–1040

Citation in format AMSBIB
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\by M.~V.~Karasev
\paper Asymptotic behavior of the spectrum of mixed states for self-consistent field equations
\jour TMF
\yr 1984
\vol 61
\issue 1
\pages 118--127
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=774212}
\zmath{https://zbmath.org/?q=an:0561.58042}
\transl
\jour Theoret. and Math. Phys.
\yr 1984
\vol 61
\issue 1
\pages 1034--1040
\crossref{https://doi.org/10.1007/BF01038552}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. V. Karasev, V. P. Maslov, “Asymptotic and geometric quantization”, Russian Math. Surveys, 39:6 (1984), 133–205  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. M. V. Karasev, “Analogues of the objects of Lie group theory for nonlinear Poisson brackets”, Math. USSR-Izv., 28:3 (1987), 497–527  mathnet  crossref  mathscinet  zmath
    3. M. V. Karasev, “Poisson symmetry algebras and the asymptotics of spectral series”, Funct. Anal. Appl., 20:1 (1986), 17–26  mathnet  crossref  mathscinet  zmath  isi
    4. M. V. Karasev, “Lagrangian rings. Multiscale asymptotics of a spectrum near resonance”, Funct. Anal. Appl., 21:1 (1987), 68–70  mathnet  crossref  mathscinet  zmath  isi
    5. M. V. Karasev, A. V. Pereskokov, “Quantization rule for self-consistent field equations with local rapidly decreasing nonlinearity”, Theoret. and Math. Phys., 79:2 (1989), 479–486  mathnet  crossref  mathscinet  isi
    6. M. V. Karasev, E. M. Novikova, “Representation of exact and semiclassical eigenfunctions via coherent states. Hydrogen atom in a magnetic field”, Theoret. and Math. Phys., 108:3 (1996), 1119–1159  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. M. V. Karasev, A. V. Pereskokov, “Asymptotic solutions of Hartree equations concentrated near low-dimensional submanifolds. I. The model with logarithmic singularity”, Izv. Math., 65:5 (2001), 883–921  mathnet  crossref  crossref  mathscinet  zmath
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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