Synchronized states of one dimensional long-range systems induced by inelastic collisions

Abstract

We report results of numerical experiments which show that a family of simple one dimensional particle systems with long-range interactions, when subjected to a certain class of inelastic interaction, evolve towards states which are highly ordered in phase space, displaying particle motions which are periodic and synchronized in relative phase. For the case of a self-gravitating system, the resulting states show a remarkable stability when the inelastic interactions are turned off, with the phase space order persisting on the longest times we simulate, and much longer than the time-scale expected for relaxation of non-equilibrium states of this long-range system to thermal equilibrium. This appears to provide a novel example of ergodicity breaking in long-range systems. We propose some simple heuristic arguments which predict reasonably well properties of the synchronized states. We enlarge our study to a broader class of long-range interacting systems, where the phenomenon of synchronisation is still present, but only for systems less than a critical size. We conclude with a discussion of avenues for further investigation.