Relaxation of quasi-stationary states in long range interacting systems and a classification of the range of pair interactions

Systems of particles interacting with long range interactions present generically "quasi-stationary states" (QSS), which are approximately time-independent out of equilibrium states. In this proceedings, we explore the generalization of the formation of such QSS and their relaxation from the much studied case of gravity to a generic pair interaction with the asymptotic form of the potential v(r) similar to 1/r (gamma) with gamma > 0 in d dimensions. We compute analytic estimations of the relaxation time calculating the rate of two body collisionality in a virialized system approximated as homogeneous. We show that for gamma < (d - 1/2), the collision integral is dominated by the size of the system, while for gamma > (d - 1/2), it is dominated by small impact parameters. In addition, the lifetime of QSS increases with the number of particles if gamma < d - 1 (i.e. the force is not integrable) and decreases if gamma > d - 1. Using numerical simulations we confirm our analytic results. A corollary of our work gives a "dynamical" classification of interactions: the dynamical properties of the system depend on whether the pair force is integrable or not.