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

TL;DR

This study experimentally tests a theoretical lower bound on four-point dynamical susceptibility in a granular packing, revealing a tight bound that captures the non-monotonic behavior across the jamming transition and links anomalous diffusion to dynamical heterogeneity.

Contribution

The paper derives a general bound on dynamical susceptibility applicable to granular systems and experimentally verifies its tightness across the jamming transition.

Findings

The bound accurately reproduces the non-monotonic behavior of dynamical susceptibility.

A connection between anomalous diffusion and dynamical heterogeneity is established.

The bound is tight in the experimental granular system.

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.