Quasi-stationary states and the range of pair interactions

Details Quasi-stationary states and the range of pair interactions Quasi-stationary states and the range of pair interactions

2010-04-28

arxiv.org/abs/1004.5119v2

Phys.Rev.Lett.105:210602,2010

Physics

Condensed Matter

Statistical Mechanics

5 pages, 3 figures; final version to appear in Phys. Rev. Lett

Scientific paper

10.1103/PhysRevLett.105.210602

"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.

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