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Mat. Sb., 1998, Volume 189, Number 6, Pages 85–116 (Mi msb325)  

This article is cited in 5 scientific papers (total in 6 papers)

Quasi-classical asymptotics of quasi-particles

V. P. Maslov, A. S. Mishchenko

M. V. Lomonosov Moscow State University

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.

DOI: https://doi.org/10.4213/sm325

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English version:
Sbornik: Mathematics, 1998, 189:6, 901–930

Bibliographic databases:

UDC: 517.9
MSC: Primary 81S30, 81Q20; Secondary 35S10, 82D50, 35P20, 81U30
Received: 18.04.1997

Citation: V. P. Maslov, A. S. Mishchenko, “Quasi-classical asymptotics of quasi-particles”, Mat. Sb., 189:6 (1998), 85–116; Sb. Math., 189:6 (1998), 901–930

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. A. A. Bolibrukh, A. A. Irmatov, M. I. Zelikin, O. B. Lupanov, V. M. Maynulov, E. F. Mishchenko, M. M. Postnikov, Yu. P. Solov'ev, E. V. Troitskii, “Aleksandr Sergeevich Mishchenko (on his 60th birthday)”, Russian Math. Surveys, 56:6 (2001), 1187–1191  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. V. V. Belov, O. S. Dobrokhotov, S. Yu. Dobrokhotov, “Isotropic Tori, Complex Germ and Maslov Index, Normal Forms and Quasimodes of Multidimensional Spectral Problems”, Math. Notes, 69:4 (2001), 437–466  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. V. P. Maslov, “Taking into Account the Interaction between Particles in the New Nucleation Theory, Quasiparticles, Quantization of Vortices, and the Two-Particle Distribution Function”, Math. Notes, 83:6 (2008), 790–803  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. V. P. Maslov, “Fluid thermodynamics, energy redistribution law, two-dimensional condensate, and $T$ map”, Theoret. and Math. Phys., 161:3 (2009), 1681–1713  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    5. Maslov V., “Dequantization, Statistical Mechanics and Econophysics”, Tropical and Idempotent Mathematics, Contemporary Mathematics, 495, 2009, 239–279  crossref  mathscinet  zmath  isi
    6. V. P. Maslov, “A new approach to phase transitions, thermodynamics, and hydrodynamics”, Theoret. and Math. Phys., 165:3 (2010), 1699–1720  mathnet  crossref  crossref  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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