期刊
EUROPEAN PHYSICAL JOURNAL B
卷 57, 期 4, 页码 391-409出版社
SPRINGER
DOI: 10.1140/epjb/e2007-00187-2
关键词
-
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.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据