Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2010-04-13
J.Stat.Mech.1010:P10012,2010
Physics
Condensed Matter
Statistical Mechanics
37 pages, 24 figures; some additional discussion of previous literature and other minor modifications, final published version
Scientific paper
10.1088/1742-5468/2010/10/P10012
We revisit the issue of relaxation to thermal equilibrium in the so-called "sheet model", i.e., particles in one dimension interacting by attractive forces independent of their separation. We show that this relaxation may be very clearly detected and characterized by following the evolution of order parameters defined by appropriately normalized moments of the phase space distribution which probe its entanglement in space and velocity coordinates. For a class of quasi-stationary states which result from the violent relaxation of rectangular waterbag initial conditions, characterized by their virial ratio R_0, we show that relaxation occurs on a time scale which (i) scales approximately linearly in the particle number N, and (ii) shows also a strong dependence on R_0, with quasi-stationary states from colder initial conditions relaxing much more rapidly. The temporal evolution of the order parameter may be well described by a stretched exponential function. We study finally the correlation of the relaxation times with the amplitude of fluctuations in the relaxing quasi-stationary states, as well as the relation between temporal and ensemble averages.
Joyce Michael
Worrakitpoonpon Tirawut
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