Lower bound on the four-point dynamical susceptibility: Direct experimental test on a granular packing

Abstract

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.

5 pages, 3 figures

References in corpus (12)

• Random Packings of Frictionless Particles
• Geometrical explanation and scaling of dynamical heterogeneities in glass forming systems
• Inhomogeneous Mode-Coupling Theory and Growing Dynamic Length in Supercooled Liquids
• Dynamical Heterogeneity close to the Jamming Transition in a Sheared Granular Material
• Heterogeneous Diffusion in Highly Supercooled Liquids
• Spatial correlations in the dynamics of glassforming liquids: Experimental determination of their temperature dependence
• Spontaneous and induced dynamic fluctuations in glass-formers I: General results and dependence on ensemble and dynamics
• Time Resolved Correlation measurements of temporally heterogeneous dynamics
• Growing Correlation Length on Cooling Below the Onset of Caging in a Simulated Glass-Forming Liquid
• Heterogeneous Dynamics of Coarsening Systems
• On the approach to equilibrium of an Hamiltonian chain of anharmonic oscillators
• Non-equilibrium temperatures in steady-state systems with conserved energy

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• Elementary Excitation Modes in a Granular Glass above Jamming
• The Jamming point street-lamp in the world of granular media
• Diverging length scale of the inhomogeneous mode-coupling theory: a numerical investigation
• Strong Dynamical Heterogeneity and Universal Scaling in Driven Granular Fluids
• Super-diffusion around the rigidity transition: Levy and the Lilliputians
• The glass transition in molecules, colloids and grains: universality and specificity
• Yield stress in amorphous solids: A mode-coupling theory analysis
• Analytical Calculation of Four-Point Correlations for a Simple Model of Cages Involving Numerous Particles
• Melting a granular glass by cooling