Tetsuro KONISHI

R-Lab., Department of Physics, 
School of Science, 
Nagoya University
Nagoya, 464-01 JAPON
tkonishi@allegro.phys.nagoya-u.ac.jp
 

Itinerant behavior in 1-dimensional mass-sheet model

Abstract: Long time behavior of Hamiltonian systems with many degrees of freedom are often well described by classical statistical mechanics. This implies that we observe simple diffusive behavior for those systems. On the other hand, there are many Hamiltonian systems which are chaotic and at the same time do not relax to thermal equilibrium uniformly. They have several states which are macroscopically distinguishable and their equations of motion take them from one state to another by purely deterministic way. This itinerant behavior is significant in the understanding of Hamiltonian chaos for many degrees of freedom. Physical examples are found in microclusters, gravitational systems, and so on. The itinerant behavior is different from 1/f-type long time tail behavior, because the long time tail is considered to be caused by motions trapped to local hierarchy of KAM tori and islands, whereas the itinerancy takes the systems to various parts in the whole phase space. We introduce several models which show the itinerant behaviors. One is a simplectic coupled map which have finite range interaction, which shows collision and reconfiguration of clusters. Another is one-dimensional self-gravity model (``sheet model''). We numerically analyse the dynamics of these models. Non-thermal transition among states are found, and relation to phase space structure is discussed. For the sheet model, we found that mechanism which trigger the itinerancy is resonance between particles and mean field potential.