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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:
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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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Linking options:
http://mi.mathnet.ru/eng/tmf5964https://doi.org/10.4213/tmf5964 http://mi.mathnet.ru/eng/tmf/v150/i1/p26
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:
-
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
-
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
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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
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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
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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.
 -
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
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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
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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
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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
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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
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