Kinetic Heterogeneities at Dynamical Crossovers

We perform molecular dynamics simulations of a model glass-forming liquid to measure the size of kinetic heterogeneities, using a dynamic susceptibility ${\chi }_{\mathrm{s}\mathrm{s}}(a,t)$ that quantifies the number of particles whose dynamics are correlated on the length scale $a$ and time scale $t$. By measuring ${\chi }_{\mathrm{s}\mathrm{s}}(a,t)$ as a function of both $a$ and $t$, we locate local maxima ${\chi }^{\star }$ at distances $a^{\star }$ and times $t^{\star }$. Near the dynamical glass transition, we find two types of maxima, both correlated with crossovers in the dynamical behavior: a smaller maximum corresponding to the crossover from ballistic to sub-diffusive motion, and a larger maximum corresponding to the crossover from sub-diffusive to diffusive motion. Our results indicate that kinetic heterogeneities are not necessarily signatures of an impending glass or jamming transition.