Active cage model of glassy dynamics

TL;DR

This paper introduces a phenomenological active cage model that captures key glassy dynamics features, including scale invariance and exponential tails, by modeling a tracer's effective confined motion with random hops, highlighting two key dimensionless parameters.

Contribution

It presents a minimal active cage model that reproduces glassy dynamics features and identifies two key parameters controlling the onset of glassy behavior.

Findings

Scale invariance in small-displacement distribution

Exponential tails as crossover between Gaussian regimes

Glassy behavior controlled by two dimensionless numbers

Abstract

We build up a phenomenological picture in terms of the effective dynamics of a tracer confined in a cage experiencing random hops to capture somec haracteristics of glassy systems. This minimal description exhibits scale invariance properties for the small-displacement distribution that echo experimental observations. We predict the existence of exponential tails as a cross-over between two Gaussian regimes. Moreover, we demonstrate that the onset of glassy behavior is controlled only by two dimensionless numbers: the number of hops occurring during the relaxation of the particle within a local cage, and the ratio of the hopping length to the cage size.