Self-Organized Bottleneck in Energy Relaxation

We study an energy relaxation process after many degrees of freedom are excited in a Hamiltonian system with a large number of degrees of freedom. Bottlenecks of relaxation, where relaxations of the excited elements are drastically slowed down, are discovered. By defining an internal state for the excited degrees of freedom, it is shown that the drastic slowing down occurs when the internal state is in a critical state. The relaxation dynamics brings the internal state into the critical state, and the critical bottleneck of relaxation is self-organized. Relevance of our result to relaxation phenomena in condensed matters or large molecules is briefly discussed.