Critical Behavior of a Heavy Particle in a Granular Fluid

Details Critical Behavior of a Heavy Particle in a Granular Fluid Critical Behavior of a Heavy Particle in a Granular Fluid

2001-02-05

arxiv.org/abs/cond-mat/0102087v1

Phys. Rev. Lett. 86, 4823-4826 (2001)

Physics

Condensed Matter

Statistical Mechanics

4 pages (4 figures included)

Scientific paper

10.1103/PhysRevLett.86.4823

Behavior analogous to a second order phase transition is observed for the homogeneous cooling state of a heavy impurity particle in a granular fluid. The order parameter $\phi $ is the ratio of impurity mean square velocity to that of the fluid, with a conjugate field $h$ proportional to the mass ratio. A parameter $\beta $, measuring the fluid cooling rate relative to the impurity--fluid collision rate, is the analogue of the inverse temperature. For $\beta <1$ the fluid is ``normal'' with $\phi =0$ at $h=0$, as in the case of a system with elastic collisions. For $\beta >1$ an ``ordered'' state with $\phi \neq 0$ occurs at $h=0$, representing an extreme breakdown of equipartition. Critical slowing and qualitative changes in the velocity distribution function for the impurity particle near the transition are noted

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