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 τ_ατ_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 τ_ατ_D∝⟨t_p⟩⟨t_c⟩, where ⟨t_p⟩ and ⟨t_c⟩ 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 τ_α∝⟨t_p⟩⟨Δr_J ²⟩ and τ_D∝⟨t_c⟩⟨Δr_J ²⟩ effectively connect the macroscopic and microscopic timescales, with the mean square jump length ⟨Δr_J ²⟩ 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.