Molecular random walks and invariance group of the Bogolyubov equation

Details Molecular random walks and invariance group of the Bogolyubov equation Molecular random walks and invariance group of the Bogolyubov equation

2009-08-03

arxiv.org/abs/0908.0274v1

Physics

Condensed Matter

Statistical Mechanics

23 pages, no figures, LaTeX AMSART, author's translation from Russian of the paper accepted to the TMPh (``Theoretical and mat

Scientific paper

Statistics of molecular random walks in a fluid is considered with the help of the Bogolyubov equation for generating functional of distribution functions. An invariance group of solutions to this equation as functions of the fluid density is discovered. It results in many exact relations between probability distribution of the path of a test particle and its irreducible correlations with the fluid. As the consequence, significant restrictions do arise on possible shapes of the path distribution. In particular, the hypothetical Gaussian form of its long-range asymptotic proves to be forbidden (even in the Boltzmann-Grad limit). Instead, a diffusive asymptotic is allowed which possesses power-law long tail (cut off by ballistic flight length).

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