Quasistationary States and the Range of Pair Interactions

``Quasistationary'' states are approximately time independent out of equilibrium states which have been observed in a variety of systems of particles interacting by long-range interactions. We investigate here the conditions of their occurrence for a generic pair interaction V(r→∞)~1/r^γ with γ>0, in $d>1$ dimensions. We generalize analytic calculations known for gravity in $d=3$ to determine the scaling parametric dependences of their relaxation rates due to two-body collisions, and report extensive numerical simulations testing their validity. Our results lead to the conclusion that, for γ<d-1, the existence of quasistationary states is ensured by the large distance behavior of the interaction alone, while for γ>d-1 it is conditioned on the short distance properties of the interaction, requiring the presence of a sufficiently large soft core in the interaction potential.