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

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, ${\tau }_p={\tau }_c^{\gamma }$, 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.

11 pages, 9 figures

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