Exact solution of a one-dimensional Boltzmann equation for a granular tracer particle

Details Exact solution of a one-dimensional Boltzmann equation for a granular tracer particle Exact solution of a one-dimensional Boltzmann equation for a granular tracer particle

2006-02-23

arxiv.org/abs/cond-mat/0602558v2

Physics

Condensed Matter

Statistical Mechanics

17 pages, 3 figures, Accepted in Physica A

Scientific paper

10.1016/j.physa.2006.04.059

We consider a one-dimensional system consisting of a granular tracer particle of mass $M$ in a bath of thermalized particles each of mass $m$. When the mass ratio, $M/m$, is equal to the coefficient of restitution, $\alpha$, the system maps to a a one-dimensional elastic gas. In this case, Boltzmann equation can be solved exactly. We also obtain expressions for the velocity autocorrelation function and the diffusion coefficient. Numerical simulations of the Boltzmann equation are performed for $M/m\neq \alpha$ where no analytical solution is available. It appears that the dynamical features remain qualitatively similar to those found in the exactly solvable case.

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