Lower bound on the four-point dynamical susceptibility: Direct experimental test on a granular packingF. Lechenault1, O. Dauchot1, G. Biroli2 and J. P. Bouchaud3
1 CEA Saclay/SPEC, URA2464 - L'Orme des Merisiers, 91191 Gif-sur-Yvette, France, EU
2 CEA Saclay/SPhT, UMR2306 - L'Orme des Merisiers, 91191 Gif-sur-Yvette, France, EU
3 Science & Finance, Capital Fund Management - 6-8 Bd. Haussmann, 75009 Paris, France, EU
received 12 December 2007; accepted in final form 25 June 2008; published August 2008
published online 4 August 2008
We track the motion of a horizontally vibrated amorphous assembly of bidisperse hard disks, for densities ranging across the jamming transition. We derive on very general grounds a bound on the dynamical susceptibility in terms of the response of the dynamics to a change in density. This generalizes a similar bound recently derived for equilibrium liquids. We find that in our experimental system the bound is tight and reproduces the non-monotonic behavior of the dynamical susceptibility both in time and density across the jamming transition. The underlying scaling behavior reveals an intimate connection between anomalous diffusion and dynamical heterogeneity.
64.70.P- - Glass transitions of specific systems.
05.40.Ca - Noise.
45.70.Cc - Static sandpiles; granular compaction.
© EPLA 2008