Algebraic Correlation Function and Anomalous Diffusion in the HMF model

Yoshiyuki Yamaguchi (1) , Freddy Bouchet (2) , Thierry Dauxois (3)

1 Department of Applied Mathematics and Physics [Kyoto]
2 INLN - Institut Non Linéaire de Nice Sophia-Antipolis
3 Phys-ENS - Laboratoire de Physique de l'ENS Lyon

In the quasi-stationary states of the Hamiltonian Mean-Field model, we numerically compute correlation functions of momenta and diffusion of angles with homogeneous initial conditions. This is an example, in a N-body Hamiltonian system, of anomalous transport properties characterized by non exponential relaxations and long-range temporal correlations. Kinetic theory predicts a striking transition between weak anomalous diffusion and strong anomalous diffusion. The numerical results are in excellent agreement with the quantitative predictions of the anomalous transport exponents. Noteworthy, also at statistical equilibrium, the system exhibits long-range temporal correlations: the correlation function is inversely proportional to time with a logarithmic correction instead of the usually expected exponential decay, leading to weak anomalous transport properties.

Mots clés: Long-range interaction; Nonequilibrium physics; Correlations

Domaines: Mécanique statistique [cond-mat.stat-mech]

Yoshiyuki Yamaguchi, Freddy Bouchet, Thierry Dauxois. Algebraic Correlation Function and Anomalous Diffusion in the HMF model. Journal of Statistical Mechanics: Theory and Experiment, 2007, P01020 (1), pp.P01020. ⟨10.1088/1742-5468/2007/01/P01020⟩. ⟨ensl-00123263⟩