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The breakdown of the Stokes-Einstein (SE) law in fragile glassformers isexamined by Molecular-Dynamics simulations of atomic liquids and polymers andconsideration of the experimental data concerning the archetypical OTPglassformer. All the four systems comply with the universal scaling between theviscosity (or the structural relaxation) and the Debye-Waller factor $\langleu^2\rangle$, the mean square amplitude of the particle rattling in the cageformed by the surrounding neighbors. It is found that the SE breakdown isscaled in a master curve by a reduced $\langle u^2\rangle$. Two approximatedexpressions of the latter, with no and one adjustable parameters respectively,are derived.

Fast dynamics perspective on the breakdown of the Stokes-Einstein law in fragile glassformers