RELAXATION PROCESSES IN ONE-DIMENSIONAL SELF-GRAVITATING MANY-BODY SYSTEMS

Though one-dimensional self-gravitating N-body systems have been studi ed for three decades, the nature of relaxation is still unclear. There have been inconsistent results regarding the relaxation time; some in itial states seemed to relax in the time scale T similar to N t(c), bu t other states did not relax even after T similar to N-2 t(c), where t (c) is the crossing time. The water-bag distribution was believed not to relax after T similar to N-2 t(c). In a previous paper, however [Ph ys. Rev. E 50, 2607 (1994)] we found that there are two different rela xation times in the water-bag distribution; in the faster relaxation ( microscopic relaxation) the equipartition of energy distribution is at tained but the macroscopic distribution turns into the isothermal dist ribution in the later relaxation (macroscopic relaxation). In this pap er, we investigate the properties of the two relaxations. We find that the microscopic relaxation time is T similar to N t(c), and the macro scopic relaxation has the much longer time scale 4 x 10(4) N t(c), thu s the water bag does relax. We can see that the inconsistency about th e relaxation times is resolved as we see the two different aspects of relaxation. Further, the physical mechanisms of the relaxation are pre sented.