Superdiffusion and Out-of-equilibrium Chaotic Dynamics with Many Degrees of Freedoms

TL;DR

This paper investigates how superdiffusive behavior arises transiently in a long-range interacting N-body system, linking it to Le9vy walks and phase transition phenomena, with diffusion normalizing at equilibrium.

Contribution

It reveals the connection between out-of-equilibrium superdiffusion and Le9vy walks in a classical many-body system with long-range interactions, highlighting the transient nature of anomalous diffusion.

Findings

Superdiffusion occurs only in a transient, out-of-equilibrium regime.

Superdiffusion is caused by Le9vy walks of particles.

Diffusion becomes normal at equilibrium after a diverging relaxation time.

Abstract

We study the link between relaxation to the equilibrium and anomalous superdiffusive motion in a classical N-body hamiltonian system with long-range interaction showing a second-order phase-transition in the canonical ensemble. Anomalous diffusion is observed only in a transient out-of-equilibrium regime and for a small range of energy, below the critical one. Superdiffusion is due to L\'evy walks of single particles and is checked independently through the second moment of the distribution, power spectra, trapping and walking time probabilities. Diffusion becomes normal at equilibrium, after a relaxation time which diverges with N.