The Hamiltonian Mean Field model: anomalous or normal diffusion?

TL;DR

This paper investigates the diffusion properties in the Hamiltonian Mean Field model, demonstrating analytically that the nature of diffusion depends on the autocorrelation decay, challenging previous numerical interpretations of anomalous diffusion.

Contribution

It provides an analytical criterion linking autocorrelation decay to diffusion type in the HMF model, clarifying the conditions for normal versus anomalous diffusion.

Findings

Autocorrelation fitted by q-exponential implies normal diffusion for q<2

Challenges previous numerical claims of anomalous diffusion in the HMF model

Offers analytical insight into diffusion behavior in long-range interacting systems

Abstract

We consider the out-of-equilibrium dynamics of the Hamiltonian Mean Field (HMF) model, by focusing in particular on the properties of single-particle diffusion. As we shall here demonstrate analytically, if the autocorrelation of momenta in the so-called quasi-stationary states can be fitted by a q-exponential, then diffusion ought to be normal for q<2, at variance with the interpretation of the numerical experiments proposed in Refs. A. Pluchino, A. Rapisarda, Progress in Theoretical Physics Supplement 162, 18 (2006); A. Pluchino, V. Latora, A. Rapisarda, Physica A 338, 60 (2004); A. Rapisarda, A. Pluchino, Europhysics News 36, 202 (2005).