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TMF, 2009, Volume 158, Number 2, Pages 200–213 (Mi tmf6309)  

This article is cited in 1 scientific paper (total in 1 paper)

Family of instantons of the Kraichnan model with a frozen velocity field

M. V. Komarovaa, I. S. Kremnevb, M. Yu. Nalimova

a Saint-Petersburg State University
b Institute for Analytical Instrumentation, Russian Academy of Sciences

Abstract: We find the family of instantons of the Kraichnan model with a frozen velocity field. Using these instantons, we investigate the asymptotic behavior of higher orders of the perturbation theory series constructed for the response function. We demonstrate that although the number of diagrams increases factorially with the degree of the perturbation series term, the perturbation series itself has a finite and sometimes even infinite convergence radius. We thus disprove the commonly accepted view that the type of series convergence can be determined by estimating the number of diagrams in higher orders of the perturbation theory.

Keywords: perturbation theory, higher-order asymptotic behavior, instanton, Kraichnan model, frozen velocity field

DOI: https://doi.org/10.4213/tmf6309

Full text: PDF file (451 kB)
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English version:
Theoretical and Mathematical Physics, 2009, 158:2, 167–178

Bibliographic databases:

Received: 17.01.2008
Revised: 06.06.2008

Citation: M. V. Komarova, I. S. Kremnev, M. Yu. Nalimov, “Family of instantons of the Kraichnan model with a frozen velocity field”, TMF, 158:2 (2009), 200–213; Theoret. and Math. Phys., 158:2 (2009), 167–178

Citation in format AMSBIB
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\by M.~V.~Komarova, I.~S.~Kremnev, M.~Yu.~Nalimov
\paper Family of instantons of the~Kraichnan model with a~frozen velocity field
\jour TMF
\yr 2009
\vol 158
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\pages 200--213
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\jour Theoret. and Math. Phys.
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Komarova M.V., Kremnev I.S., Nalimov M.Yu., “Convergence of perturbation series for renormalization constants in Kraichnan model with “frozen” velocity field”, Eur Phys J C Part Fields, 71:5 (2011), 1646  crossref  mathscinet  adsnasa  isi  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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