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

International audienceSystems 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 $v(r) \sim 1/r^\gamma$ 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 $\gamma (d-1/2)$, it is dominated by small impact parameters. In addition, the lifetime of QSS increases with the number of particles 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