Relaxation times of unstable states in systems with long range interactions

Details Relaxation times of unstable states in systems with long range interactions Relaxation times of unstable states in systems with long range interactions

2007-09-10

arxiv.org/abs/0709.1361v2

J. Stat. Mech. (2007) P11008

Physics

Condensed Matter

Statistical Mechanics

Minor changes

Scientific paper

10.1088/1742-5468/2007/11/P11008

We consider several models with long-range interactions evolving via Hamiltonian dynamics. The microcanonical dynamics of the basic Hamiltonian Mean Field (HMF) model and perturbed HMF models with either global anisotropy or an on-site potential are studied both analytically and numerically. We find that in the magnetic phase, the initial zero magnetization state remains stable above a critical energy and is unstable below it. In the dynamically stable state, these models exhibit relaxation time scales that increase algebraically with the number $N$ of particles, indicating the robustness of the quasistationary state seen in previous studies. In the unstable state, the corresponding time scale increases logarithmically in $N$.

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