Super-diffusion around the rigidity transition: Levy and the Lilliputians

TL;DR

This study demonstrates that near the jamming transition, granular particles exhibit superdiffusive Levy flight behavior with small jumps, transitioning to normal diffusion as the system moves away from criticality.

Contribution

It provides experimental evidence that superdiffusion in vibrated granular media is due to Levy flights caused by micro-crack events, challenging previous interpretations based on vibrational modes.

Findings

Superdiffusive motion is a genuine Levy flight with small jumps.

Jump size distribution is truncated away from the jamming point, leading to normal diffusion.

Micro-crack events at all scales drive the Levy flight behavior.

Abstract

By analyzing the displacement statistics of an assembly of horizontally vibrated bidisperse frictional grains in the vicinity of the jamming transition experimentally studied before, we establish that their superdiffusive motion is a genuine Levy flight, but with `jump' size very small compared to the diameter of the grains. The vibration induces a broad distribution of jumps that are random in time, but correlated in space, and that can be interpreted as micro-crack events at all scales. As the volume fraction departs from the critical jamming density, this distribution is truncated at a smaller and smaller jump size, inducing a crossover towards standard diffusive motion at long times. This interpretation contrasts with the idea of temporally persistent, spatially correlated currents and raises new issues regarding the analysis of the dynamics in terms of vibrational modes.