Hard-sphere Brownian motion in ideal gas: inter-particle correlations, Boltzmann-Grad limit, and destroying the myth of molecular chaos propagation

Details Hard-sphere Brownian motion in ideal gas: inter-particle correlations, Boltzmann-Grad limit, and destroying the myth of molecular chaos propagation Hard-sphere Brownian motion in ideal gas: inter-particle correlations, Boltzmann-Grad limit, and destroying the myth of molecular chaos propagation

2010-01-10

arxiv.org/abs/1001.1558v1

Physics

Condensed Matter

Statistical Mechanics

6 pages, 1 figure, latex revtex4-1

Scientific paper

The BBGKY hierarchy of equations for a particle interacting with ideal gas is analyzed in terms of irreducible many-particle correlations between gas atoms and the particle's motion. The transition to the hard-sphere interaction is formulated from viewpoint of the recently discovered exact relations connecting the correlations with the particle's probability distribution. Then the Boltzmann-Grad limit is considered and shown not to lead to the Bolzmann hierarchy and the molecular chaos, since correlations of all orders keep significant.in this limit, merely taking a singular form.

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