Simple Model for Dynamic Heterogeneity in Glass-Forming Liquids

Liquids near the glass transition exhibit dynamical heterogeneity, i.e., local relaxation rates fluctuate strongly over space and time. Here, we introduce a simple continuum model that allows for quantitative predictions for the correlators describing these fluctuations. We find remarkable agreement of the model predictions for the dynamic susceptibility chi 4(t) with numerical results for a binary hard-sphere liquid and for a Kob-Andersen Lennard-Jones mixture. Under this model, the lifetime tau ex of the heterogeneities has little effect on the position t = t4 similar to tau alpha of the peak of chi 4(t), but it controls the decay of chi 4(t) after the peak, and we show how to estimate it from this decay.