Chaotic Itinerancy and Thermalization in One-dimensional Self-gravitating Systems

This is the third paper of the series of our studies of the one-dimensional selfgravitating many-body systems. In our rst paper (Paper I), we found there are two stages in the relaxation of the water-bag to isothermal distribution, the microscopic relaxation and the macroscopic relaxation as the faster and the slower relaxation, respectively. In the second paper (Paper II), we derived the time scales of the relaxations numerically, and discussed the mechanisms, for the water-bag distribution. After these paper, we found phenomena that the system returns from the isothermal distribution to the water-bag. Thus the time scale of the macroscopic relaxation is found not to be su cient for true thermalization. In this paper, we thus study the transition phenomena after the rst transition from a quasiequilibrium. We found that irrespective of the initial conditions, the system wanders between many states which yield the same properties of the quasiequilibrium as the water-bag. This itinerancy is most prominent in the time scale t 10 5 10 6 t c . In the midway between two succeeding quasiequilibria, the system experiences a transient state, where one particle keeps exclusive high energy and its motion decouples with the Electronic address: [email protected]