Dynamical stability criterion for inhomogeneous quasi-stationary states in long-range systems

Details Dynamical stability criterion for inhomogeneous quasi-stationary states in long-range systems Dynamical stability criterion for inhomogeneous quasi-stationary states in long-range systems

2010-03-11

arxiv.org/abs/1003.2378v1

J. Stat. Mech. (2010) P06001

Physics

Condensed Matter

Statistical Mechanics

Submitted to Journal of Statistical Mechanics: Theory and Experiment

Scientific paper

We derive a necessary and sufficient condition of linear dynamical stability for inhomogeneous Vlasov stationary states of the Hamiltonian Mean Field (HMF) model. The condition is expressed by an explicit disequality that has to be satisfied by the stationary state, and it generalizes the known disequality for homogeneous stationary states. In addition, we derive analogous disequalities that express necessary and sufficient conditions of formal stability for the stationary states. Their usefulness, from the point of view of linear dynamical stability, is that they are simpler, although they provide only sufficient criteria of linear stability. We show that for homogeneous stationary states the relations become equal, and therefore linear dynamical stability and formal stability become equivalent.

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