M. V. Karasev, A. V. Pereskokov, “Logarithmic corrections in a quantization rule. The polaron spectrum”, TMF, 97:1 (1993), 78–93; Theoret. and Math. Phys., 97:1 (1993), 1160

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Teoreticheskaya i Matematicheskaya Fizika, 1993, Volume 97, Number 1, Pages 78–93 (Mi tmf1725)

This article is cited in 9 scientific papers (total in 9 papers)

Logarithmic corrections in a quantization rule. The polaron spectrum

M. V. Karasev^a, A. V. Pereskokov^b

^a Moscow State Institute of Electronics and Mathematics
^b Moscow Power Engineering Institute (Technical University)

Full-text PDF (1273 kB) Citations (9)

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Abstract: A nonlinear integrodifferential equation that arises in polaron theory is considered. The integral nonlinearity is given by a convolution with the Coulomb potential. Radially symmetric solutions are sought. In the semiclassical limit, an equation for the self-consistent potential is found and studied. The potential has a logarithmic singularity at the origin, and also a turning point at 1. The phase shifts at these points are determined. The quantization rule that takes into account the logarithmic corrections gives a simple asymptotic formula for the polaron spectrum. Global semiclassical solutions of the original nonlinear equation are constructed.

Received: 20.11.1992

English version:
Theoretical and Mathematical Physics, 1993, Volume 97, Issue 1, Pages 1160–1170
DOI: https://doi.org/10.1007/BF01014809

Bibliographic databases:

Language: Russian

Citation: M. V. Karasev, A. V. Pereskokov, “Logarithmic corrections in a quantization rule. The polaron spectrum”, TMF, 97:1 (1993), 78–93; Theoret. and Math. Phys., 97:1 (1993), 1160–1170

Citation in format AMSBIB

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\paper Logarithmic corrections in a~quantization rule. The polaron spectrum

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\transl

\jour Theoret. and Math. Phys.

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\vol 97

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\pages 1160--1170

\crossref{https://doi.org/10.1007/BF01014809}

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Linking options:

https://www.mathnet.ru/eng/tmf1725

https://www.mathnet.ru/eng/tmf/v97/i1/p78

This publication is cited in the following 9 articles:

A. V. Pereskokov, “Semiclassical asymptotic spectrum of the two-dimensional Hartree operator near a local maximum of the eigenvalues in a spectral cluste”, Theoret. and Math. Phys., 205:3 (2020), 1652–1665
Lipskaya A.V., Pereskokov A.V., “Ob asimptoticheskikh resheniyakh uravneniya tipa khartri s potentsialom vzaimodeistviya yukavy, sosredotochennykh v share”, Vestnik Moskovskogo energeticheskogo instituta, 2011, no. 6, 30–38 On asymptotic solutions concentrated in a ball of the hartree-type equation with the yukawa interaction potential
Efremov G.F., Petrov D.A., Maslov A.O., “Fononnoe trenie i provodimost kristallov”, Vestnik nizhegorodskogo universiteta im. N.I. Lobachevskogo, 2011, no. 4-1, 36–42 Phonon damping and crystal conductivity
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”, Theoret. and Math. Phys., 150:1 (2007), 21–33
M. V. Karasev, A. V. Pereskokov, “Asymptotic solutions for Hartree equations and logarithmic obstructions for higher corrections of semiclassical approximation”, Proc. Steklov Inst. Math. (Suppl.), 2003no. , suppl. 1, S123–S128
V. V. Belov, A. Yu. Trifonov, A. V. Shapovalov, “Semiclassical Trajectory-Coherent Approximations of Hartree-Type Equations”, Theoret. and Math. Phys., 130:3 (2002), 391–418
A. V. Pereskokov, “Asymptotic Solutions of Two-Dimensional Hartree-Type Equations Localized in the Neighborhood of Line Segments”, Theoret. and Math. Phys., 131:3 (2002), 775–790
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. V. Karasev, A. V. Pereskokov, “Asymptotic solutions of Hartree equations concentrated near low-dimensional submanifolds. II. Localization in planar discs”, Izv. Math., 65:6 (2001), 1127–1168

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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