Equilibrium Distribution of Heavy Quarks in Fokker-Planck Dynamics

Details Equilibrium Distribution of Heavy Quarks in Fokker-Planck Dynamics Equilibrium Distribution of Heavy Quarks in Fokker-Planck Dynamics

1999-07-07

arxiv.org/abs/hep-ph/9907273v1

Phys.Rev.Lett. 84 (2000) 31-34

Physics

High Energy Physics

High Energy Physics - Phenomenology

4 pages including 2 figures

Scientific paper

10.1103/PhysRevLett.84.31

We obtain within Fokker-Planck dynamics an explicit generalization of Einstein's relation between drag, diffusion and equilibrium distribution for a spatially homogeneous system, considering both the transverse and longitudinal diffusion for dimension n>1. We then provide a complete characterization of when the equilibrium distribution becomes a Boltzmann/J"uttner distribution, and when it satisfies the more general Tsallis distribution. We apply this analysis to recent calculations of drag and diffusion of a charm quark in a thermal plasma, and show that only a Tsallis distribution describes the equilibrium distribution well. We also provide a practical recipe applicable to highly relativistic plasmas, for determining both diffusion coefficients so that a specific equilibrium distribution will arise for a given drag coefficient.

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