A 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 ${\tau }_{\mathrm{e}\mathrm{x}}$ of the heterogeneities has little effect on the position $t=t_4\sim {\tau }_{\alpha }$ 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.