Anomalous diffusion as a signature of a collapsing phase in two-dimensional self-gravitating systems

A two-dimensional self-gravitating Hamiltonian model made by N fully coupled classical particles exhibits a transition from a collapsing phase (CP) at low energy to a homogeneous phase (HP) at high energy. From a dynamical point of view, the two phases are characterized by two distinct single-particle motions: namely, superdiffusive in the CP and ballistic in the HP. Anomalous diffusion is observed up to a time τ that increases linearly with N. Therefore, the finite particle number acts like a white noise source for the system, inhibiting anomalous transport at longer times.