Quasi-stationary states and the range of pair interactions
  "Quasi-stationary" 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 \rightarrow
\infty) \sim 1/r^a with a > 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 a < d-1, the existence of quasi-stationary states is
ensured by the large distance behavior of the interaction alone, while for a >
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.
