Relaxation processes in one-dimensional self-gravitating many-body systems

Details Relaxation processes in one-dimensional self-gravitating many-body systems Relaxation processes in one-dimensional self-gravitating many-body systems

1995-06-03

arxiv.org/abs/astro-ph/9506018v1

Phys.Rev. E53 (1996) 2210

Astronomy and Astrophysics

Astrophysics

11 pages, uuencoded, compressed Postscript, no figure, figures available at ftp://ferio.mtk.nao.ac.jp/pub/tsuchiya/Tsuchiya95.

Scientific paper

10.1103/PhysRevE.53.2210

Though one dimensional self-gravitating $N$-body systems have been studied for three decade, the nature of relaxation was still unclear. There were inconsistent results about relaxation time; some initial state relaxed in the time scale $T\sim N\,t_c$, but another state did not relax even after $T\sim N^2\,t_c$, where $t_c$ is the crossing time. The water-bag distribution was believed not to relax after $T\sim N^2\,t_c$. In our previous paper, however, we found there are two different relaxation times in the water-bag distribution;in the faster relaxation ( microscopic relaxation ) the equipartition of energy distribution is attains but the macroscopic distribution turns into the isothermal distribution in the later relaxation (macroscopic relaxation). In this paper, we investigated the properties of the two relaxation. We found that the microscopic relaxation time is $T\sim N\,t_c$, and the macroscopic relaxation time is proportional to $N\,t_c$, thus the water-bag does relax. We can see the inconsistency about the relaxation times is resolved as that we see the two different aspect of relaxations. Further, the physical mechanisms of the relaxations are presented.

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