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.
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
\Bibitem{Kar84}
\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
\mathnet{http://mi.mathnet.ru/tmf5664}
\mathscinet{http://mathscinet.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}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1984AGK6100011}
Linking options:
https://www.mathnet.ru/eng/tmf5664
https://www.mathnet.ru/eng/tmf/v61/i1/p118
This publication is cited in the following 8 articles:
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
M. Karasev, E. Novikova, “Coherent transform of the spectral problem and algebras with nonlinear commutation relations”, J Math Sci, 95:6 (1999), 2703
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
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
M. V. Karasev, “Lagrangian rings. Multiscale asymptotics of a spectrum near resonance”, Funct. Anal. Appl., 21:1 (1987), 68–70
M. V. Karasev, “Analogues of the objects of Lie group theory for nonlinear Poisson brackets”, Math. USSR-Izv., 28:3 (1987), 497–527
M. V. Karasev, “Poisson symmetry algebras and the asymptotics of spectral series”, Funct. Anal. Appl., 20:1 (1986), 17–26
M. V. Karasev, V. P. Maslov, “Asymptotic and geometric quantization”, Russian Math. Surveys, 39:6 (1984), 133–205
Citation in format AMSBIB
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