title: Features of statistical dynamics in a finite system.
abstract: We study features of statistical dynamics in a finite Hamilton system composed of a relevant one degree of freedom coupled to an irrelevant multidegree of freedom system through a weak interaction. Special attention is paid on how the statistical dynamics changes depending on the number of degrees of freedom in the irrelevant system. It is found that the macrolevel statistical aspects are strongly related to an appearance of the microlevel chaotic motion, and a dissipation of the relevant motion is realized passing through three distinct stages: dephasing, statistical relaxation, and equilibrium regimes. It is clarified that the dynamical description and the conventional transport approach provide us with almost the same macrolevel and microlevel mechanisms only for the system with a very large number of irrelevant degrees of freedom. It is also shown that the statistical relaxation in the finite system is an anomalous diffusion and the fluctuation effects have a finite correlation time.
authors.affiliation: Department of Mathematical Science, Ibaraki University, Mito, Ibaraki 310-8512, Japan.
authors.forename: Shiwei
authors.initials: S
authors.lastname: Yan
authors.forename: Fumihiko
authors.initials: F
authors.lastname: Sakata
authors.forename: Yizhong
authors.initials: Y
authors.lastname: Zhuo