Exact diffusion coefficient of self-gravitating Brownian particles in two dimensions

P. H. Chavanis ()

The European Physical Journal B: Condensed Matter and Complex Systems, 2007, vol. 57, issue 4, 391-409

Abstract: We derive the exact expression of the diffusion coefficient of a self-gravitating Brownian gas in two dimensions. Our formula generalizes the usual Einstein relation for a free Brownian motion to the context of two-dimensional gravity. We show the existence of a critical temperature T c at which the diffusion coefficient vanishes. For T > T c , the diffusion coefficient is negative and the gas undergoes gravitational collapse. This leads to the formation of a Dirac peak concentrating the whole mass in a finite time. We also stress that the critical temperature T c is different from the collapse temperature T * at which the partition function diverges. These quantities differ by a factor 1-1/N where N is the number of particles in the system. We provide clear evidence of this difference by explicitly solving the case N=2. We also mention the analogy with the chemotactic aggregation of bacteria in biology, the formation of “atoms” in a two-dimensional (2D) plasma and the formation of dipoles or “supervortices” in 2D point vortex dynamics. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Keywords: 05.45.-a Nonlinear dynamics and chaos, 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion, 05.20.-y Classical statistical mechanics, 04.40.-b Self-gravitating systems; continuous media and classical fields in curved spacetime, (search for similar items in EconPapers)
Date: 2007
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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DOI: 10.1140/epjb/e2007-00187-2

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