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arXiv · hep-ph/9907273

Equilibrium Distribution of Heavy Quarks in Fokker-Planck Dynamics

D. Brian Walton·Johann Rafelski
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Abstract

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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D. Brian Walton, Johann Rafelski. 1999-07-07. Equilibrium Distribution of Heavy Quarks in Fokker-Planck Dynamics. https://doi.org/10.1103/physrevlett.84.31

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