Cluster dynamics in the Hamiltonian Mean Field model
Hiroko Koyama
Abstract
We investigate and characterize the dynamical properties of cluster in the Hamiltonian Mean Field model. This model has a second-order phase transition and, in the ordered low energy phase, particles are clustered. However, when the number of particles is finite, some particles can leave the cluster and acquire a high energy. Hence, below the critical energy, the ?gfully-clustered?h and ?gexcited?h states appear by turns. We show that the numerically computed time-averaged trapping ratio agrees with that obtained by a statistical average performed for the Boltzmann-Gibbs stationary solution of the Vlasov equation. However, we found numerically that the probability distribution of the lifetime of the ?gfully-clustered?h state is not exponential but follows instead a power law. Therefore, although an average trapping ratio exists, there appear to be no typical trapping ratio in the probabilistic sense.