Real space origin of temperature crossovers in supercooled liquids

We show that the various crossovers between dynamical regimes observed in experiments and simulations of supercooled liquids can be explained in simple terms from the existence and statistical properties of dynamical heterogeneities. We confirm that dynamic heterogeneity is responsible for the slowing down of glass formers at temperatures well above the dynamic singularity $T_c$ predicted by mode-coupling theory. Our results imply that activated processes govern the long-time dynamics even in the temperature regime where they are neglected by mode-coupling theory. We show that alternative interpretations based on topographic properties of the potential energy landscape are inefficient ways of describing simple physical features which are naturally accounted for within our approach. We show in particular that the reported links between mode coupling and landscape singularities do not exist.