Super-diffusion around the rigidity transition: Levy and the Lilliputians - Lechenault, F. and Candelier, R. and Dauchot, O. and Bouchaud, J. -P. and Biroli, G.
SOFT MATTER 6, 3059-3064 (2010)
Abstract : By analyzing the displacement statistics of an assembly of horizontally
vibrated bi-disperse frictional grains in the vicinity of the jamming
transition experimentally studied before (F. Lechenault, O. Dauchot, G.
Biroli and J.-P. Bouchard, Europhys. Lett., 2008, 83, 46003), we
establish that their superdiffusive motion is a genuine Levy flight, but
with a `jump' size that is 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