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TMF, 2009, Volume 160, Number 3, Pages 517–533 (Mi tmf6413)  

This article is cited in 3 scientific papers (total in 3 papers)

Molecular random walk and a symmetry group of the Bogoliubov equation

Yu. E. Kuzovlev

Galkin Donetsk Physical and Technical Institute, National Academy of Sciences Ukraine, Donetsk, Ukraine

Abstract: We consider the statistics of molecular random walks in fluids using the Bogoliubov equation for the generating functional of the distribution functions. We obtain the symmetry group of this equation and its solutions as functions of the medium density. It induces a series of exact relations between the probability distribution of the total path of a walking test particle and its correlations with the environment and consequently imposes serious constraints on the possible form of the path distribution. In particular, the Gaussian asymptotic form of the distribution is definitely forbidden (even for the Boltzmann–Grad gas), but the diffusive asymptotic form with power-law tails (cut off by the ballistic flight length) is allowed.

Keywords: BBGKY equation, Bogoliubov generating functional, molecular random walk, diffusion, kinetic theory of gases and liquids

DOI: https://doi.org/10.4213/tmf6413

Full text: PDF file (493 kB)
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English version:
Theoretical and Mathematical Physics, 2009, 160:3, 1301–1315

Bibliographic databases:

Received: 22.07.2008
Revised: 25.12.2008

Citation: Yu. E. Kuzovlev, “Molecular random walk and a symmetry group of the Bogoliubov equation”, TMF, 160:3 (2009), 517–533; Theoret. and Math. Phys., 160:3 (2009), 1301–1315

Citation in format AMSBIB
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\paper Molecular random walk and a~symmetry group of the~Bogoliubov equation
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\jour Theoret. and Math. Phys.
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\pages 1301--1315
\crossref{https://doi.org/10.1007/s11232-009-0117-0}
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  • https://doi.org/10.4213/tmf6413
  • http://mi.mathnet.ru/eng/tmf/v160/i3/p517

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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. G. N. Bochkov, Yu. E. Kuzovlev, “Fluctuation–dissipation relations. Achievements and misunderstandings”, Phys. Usp., 56:6 (2013), 590–602  mathnet  crossref  crossref  adsnasa  isi  elib
    2. Yu. E. Kuzovlev, “Why nature needs 1/f noise”, Phys. Usp., 58:7 (2015), 719–729  mathnet  crossref  crossref  adsnasa  isi  elib  elib
    3. Yu. E. Kuzovlev, “On real statistics of relaxation in gases”, JETP Letters, 103:4 (2016), 234–237  mathnet  crossref  crossref  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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