Ergodic properties of systems with long-range interactions.

We study the ergodic properties of a two-dimensional self-gravitating system using molecular dynamics simulations by applying three different tests for ergodicity: a direct method comparing the time average of a particle momentum to ensemble averages, sojourn times statistics for cells in momentum space and the dynamical functional method. These methods are also applied to a short-range interacting system (a hard-sphers gas in two dimensions), and the Hamiltonian mean-field model, for comparison purposes. Our results show that a two-dimensional self-gravitating system takes a very long time to establish ergodicity. This time is independent of particle number, at variance with what is observed in the Hamiltonian mean-field model.