Existence of Quasi-stationary states at the Long Range threshold

Alessio Turchi (1, 2, 3) , Duccio Fanelli (2) , Xavier Leoncini (4, 1, 3)

1 CPT - Centre de Physique Théorique - UMR 6207
2 Dipartimento di Energetica “Sergio Stecco”
3 CPT - Centre de Physique Théorique - UMR 7332
4 CPT - Ex E7 Systèmes dynamiques et théorie ergodique

In this paper the lifetime of quasi-stationary states (QSS) in the $\alpha-$HMF model are investigated at the long range threshold ($\alpha=1$). It is found that QSS exist and have a diverging lifetime $\tau(N)$ with system size which scales as $\mbox{\ensuremath{\tau}(N)\ensuremath{\sim}}\log N$, which contrast to the exhibited power law for $\alpha<1$ and the observed finite lifetime for $\alpha>1$. Another feature of the long range nature of the system beyond the threshold ( $\alpha>1$) namely a phase transition is displayed for $\alpha=1.5$. The definition of a long range system is as well discussed.

Mots clés: long-range systems; Hamiltonian dynamics; thermodynamic limit

Domaines: Mécanique statistique [cond-mat.stat-mech]; Dynamique Chaotique [nlin.CD]

Alessio Turchi, Duccio Fanelli, Xavier Leoncini. Existence of Quasi-stationary states at the Long Range threshold. Commun. Nonlinear. Sci. Numer. Simulat., 2011, 16 (12), pp.4718-4724. ⟨10.1016/j.cnsns.2011.03.013⟩. ⟨hal-00499612⟩