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 χ_{4}(t) with numerical results for a binary hard-sphere liquid and for a Kob-Andersen Lennard-Jones mixture. Under this model, the lifetime τ_{ex} of the heterogeneities has little effect on the position t=t_{4}∼τ_{α} of the peak of χ_{4}(t), but it controls the decay of χ_{4}(t) after the peak, and we show how to estimate it from this decay.