Ergodicity Breaking and Parametric Resonances in Systems with Long-Range Interactions

Details Ergodicity Breaking and Parametric Resonances in Systems with Long-Range Interactions Ergodicity Breaking and Parametric Resonances in Systems with Long-Range Interactions

2012-02-08

arxiv.org/abs/1202.1810v2

Physics

Condensed Matter

Statistical Mechanics

5 pages, 3 figures, Accepted in Phys. Rev. Lett

Scientific paper

We explore the mechanism responsible for the ergodicity breaking in systems with long-range forces. In thermodynamic limit such systems do not evolve to the Boltzmann-Gibbs equilibrium, but become trapped in an out-of-equilibrium quasi-stationary-state. Nevertheless, we show that if the initial distribution satisfies a specific constraint - a generalized virial condition - the quasi- stationary-state is very close to ergodic and can be described by Lynden-Bell statistics. On the other hand if the generalized virial condition is violated, parametric resonances are excited, leading to chaos and ergodicity breaking.

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