Breakdown Of The Stokes-Einstein Relation In Supercooled Liquids: A Cage-Jump Perspective

The breakdown of the Stokes-Einstein relation in supercooled liquids, which is the increase in the ratio tau alpha tau D between the two macroscopic times for structural relaxation and diffusion on decreasing the temperature, is commonly ascribed to dynamic heterogeneities, but a clear-cut microscopic interpretation is still lacking. Here, we tackle this issue exploiting the single-particle cage-jump framework to analyze molecular dynamics simulations of soft disk assemblies and supercooled water. We find that tau alpha tau D & PROP;& lang;tp & rang;& lang;tc & rang;, where & lang;t(p)& rang; and & lang;t(c)& rang; are the cage-jump times characterizing slow and fast particles, respectively. We further clarify that this scaling does not arise from a simple term-by-term proportionality; rather, the relations tau alpha & PROP;& lang;tp & rang;& lang;& UDelta;rJ2 & rang; and tau D & PROP;& lang;tc & rang;& lang;& UDelta;rJ2 & rang; effectively connect the macroscopic and microscopic timescales, with the mean square jump length & lang;& UDelta;rJ2 & rang; shrinking on cooling. Our work provides a microscopic perspective on the Stokes-Einstein breakdown and generalizes previous results on lattice models to the case of more realistic glass-formers.