Hamiltonian Dynamics and Statistics of Relaxations

Statistics of relaxations are investigated in a Hamiltonian system which has second order phase transition. Temporal evolutions of the system are yielded by Hamiltonian equations of motion, which are numerically integrated. Anomalously slow relaxation appears near the critical point for a statistical quantity. The statistic is produced by taking average over initial conditions. Key words: Second order phase transition, critical point, slow relaxation, Hamiltonian dynamics, initial condition 1. Introduction Relaxations to the equilibrium are interesting phenomena as dynamical properties of systems which have many degrees of freedom. In particular, we are interested in relaxations in second order phase transition, since the relaxation is anomalous near the critical point. That is the system comes closer to the critical point, the relaxation is the slower. When we discuss relaxations of systems, we must get temporal evolutions of the systems. Systems having second order phase transition ..