The Vlasov equation and the Hamiltonian Mean-Field model

Details The Vlasov equation and the Hamiltonian Mean-Field model The Vlasov equation and the Hamiltonian Mean-Field model

2005-11-03

arxiv.org/abs/cond-mat/0511070v1

Physica A 365, 177-183 (2006)

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1016/j.physa.2006.01.005

We show that the quasi-stationary states observed in the $N$-particle dynamics of the Hamiltonian Mean-Field (HMF) model are nothing but Vlasov stable homogeneous (zero magnetization) states. There is an infinity of Vlasov stable homogeneous states corresponding to different initial momentum distributions. Tsallis $q$-exponentials in momentum, homogeneous in angle, distribution functions are possible, however, they are not special in any respect, among an infinity of others. All Vlasov stable homogeneous states lose their stability because of finite $N$ effects and, after a relaxation time diverging with a power-law of the number of particles, the system converges to the Boltzmann-Gibbs equilibrium.

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