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The interplay between self-diffusion and excitation lines in space-time wasrecently studied in kinetically constrained models to explain the breakdown ofthe Stokes-Einstein law in supercooled liquids. Here, we further examine thisinterplay and its manifestation in incoherent scattering functions. Inparticular, we establish a dynamic length scale below which Fickian diffusionbreaks down, as is observed in experiments and simulations. We describe thetemperature dependence of this length scale in liquids of various fragilities,and provide analytical estimates for the van Hove and self-intermediatescattering functions.Comment: v3: final versio

Length scale for the onset of Fickian diffusion in supercooled liquids