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TMF, 2007, Volume 150, Number 1, Pages 26–40 (Mi tmf5964)  

This article is cited in 10 scientific papers (total in 10 papers)

Semiclassical spectral series of a Hartree-type operator corresponding to a rest point of the classical Hamilton–Ehrenfest system

V. V. Belova, F. N. Litvinetsb, A. Yu. Trifonovb

a Moscow State Institute of Electronics and Mathematics
b Tomsk Polytechnic University

Abstract: We consider the classical equations of motion in quantum means, i.e., the Hamilton–Ehrenfest system. In the semiclassical approximation in the framework of the covariant approach based on these equations, we construct the spectral series of a nonlinear Hartree-type operator corresponding to a rest point.

Keywords: complex germ method, spectral series, Hartree equation

DOI: https://doi.org/10.4213/tmf5964

Full text: PDF file (524 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2007, 150:1, 21–33

Bibliographic databases:

Received: 26.05.2006

Citation: V. V. Belov, F. N. Litvinets, A. Yu. Trifonov, “Semiclassical spectral series of a Hartree-type operator corresponding to a rest point of the classical Hamilton–Ehrenfest system”, TMF, 150:1 (2007), 26–40; Theoret. and Math. Phys., 150:1 (2007), 21–33

Citation in format AMSBIB
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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. Belov V.V., “Semiclassical spectrum for a Hartree-type equation corresponding to a rest point of the Hamilton-Ehrenfest system”, J. Phys. A, 39:34 (2006), 10821  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. Litvinets F.N., “Berry phases for 3D Hartree-type equations with a quadratic potential and a uniform magnetic field”, J. Phys. A, 40:36 (2007), 11129  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. Belov V.V., Smirnova E.I., Trifonov A.Yu., “Semiclassical spectral series for the two-component Hartree-type equation”, Russian Phys. J., 54:6 (2011), 639–648  crossref  mathscinet  zmath  adsnasa  isi  elib  elib  scopus
    4. Lipskaya A.V., Pereskokov A.V., “Asimptoticheskie resheniya odnomernogo uravneniya Khartri s negladkim potentsialom vzaimodeistviya. Asimptotika kvantovykh srednikh”, Vestn. Mosk. energeticheskogo in-ta, 2012, no. 6, 105–116  elib
    5. Aleksandr L. Lisok, Aleksandr V. Shapovalov, Andrey Yu. Trifonov, “Symmetry and Intertwining Operators for the Nonlocal Gross–Pitaevskii Equation”, SIGMA, 9 (2013), 066, 21 pp.  mathnet  crossref  mathscinet
    6. A. V. Pereskokov, “Semiclassical asymptotic spectrum of a Hartree-type operator near the upper boundary of spectral clusters”, Theoret. and Math. Phys., 178:1 (2014), 76–92  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    7. A. V. Pereskokov, “Asymptotics of the Hartree operator spectrum near the upper boundaries of spectral clusters: Asymptotic solutions localized near a circle”, Theoret. and Math. Phys., 183:1 (2015), 516–526  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    8. A. V. Pereskokov, “Semiclassical asymptotic approximation of the two-dimensional Hartree operator spectrum near the upper boundaries of spectral clusters”, Theoret. and Math. Phys., 187:1 (2016), 511–524  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    9. A. V. Pereskokov, “Semiclassical Asymptotics of the Spectrum near the Lower Boundary of Spectral Clusters for a Hartree-Type Operator”, Math. Notes, 101:6 (2017), 1009–1022  mathnet  crossref  crossref  mathscinet  isi  elib
    10. D. A. Vakhrameeva, A. V. Pereskokov, “Asymptotics of the spectrum of a two-dimensional Hartree-type operator with a Coulomb self-action potential near the lower boundaries of spectral clusters”, Theoret. and Math. Phys., 199:3 (2019), 864–877  mathnet  crossref
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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