The relation between the structure of blocked clusters and the relaxation dynamics in kinetically-constrained models

TL;DR

This study explores the connection between cooperative length scales and relaxation times in kinetically-constrained models, revealing a power-law relation and subexponential decay of persistence functions that vary with density.

Contribution

It establishes a quantitative relation between culling and persistence times and analyzes the decay behavior of the persistence function near full density in these models.

Findings

Persistence time scales as a power of culling time, with model- and dimension-dependent exponent.

Persistence function decays subexponentially, with the decay exponent approaching zero as density approaches one.

The relation between structure and dynamics is characterized through defect diffusion mapping.

Abstract

We investigate the relation between the cooperative length and the relaxation time, represented respectively by the culling time and the persistence time, in the Fredrickson-Andersen, Kob-Andersen and spiral kinetically-constrained models. By mapping the dynamics to diffusion of defects, we find a relation between the persistence time, $\tau_{p}$, which is the time until a particle moves for the first time, and the culling time, $\tau_{c}$, which is the minimal number of particles that need to move before a specific particle can move, $\tau_{p}=\tau^{\gamma}_{c}$, where $\gamma$ is model- and dimension dependent. We also show that the persistence function in the Kob-Andersen and Fredrickson-Andersen models decays subexponentially in time, $P(t)=exp[-(t/\tau)^{\beta}]$, but unlike previous works we find that the exponent $\beta$ appears to decay to 0 as the particle density approaches 1.