ANOMALOUS DIFFUSION AS A SIGNATURE OF A COLLAPSING PHASE IN 2-DIMENSIONAL SELF-GRAVITATING SYSTEMS

A two-dimensional self-gravitating Hamiltonian model made by N fully c oupled classical particles exhibits a transition from a collapsing pha se (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 di stinct single-particle motions: namely, superdiffusive in the CP and b allistic in the HP. Anomalous diffusion is observed up to a time tau t hat increases linearly with N. Therefore, the finite particle number a cts like a white noise source for the system, inhibiting anomalous tra nsport at longer times.