Communication: Fast and local predictors of the violation of the Stokes-Einstein law in polymers and supercooled liquids.

The violation of the Stokes-Einstein (SE) law is investigated in a melt of linear chains by extensive molecular-dynamics simulations. It is found that the SE breakdown is signaled (with 5% uncertainty) by the monomer mean-square displacement <u(2)> on the picosecond time scale. On this time scale the displacements of the next-next-nearest neighbors are uncorrelated. It is shown that: (i) the SE breakdown occurs when <u(2)> is smaller than the breadth of the distribution of the square displacements to escape from the first-neighbors cage, (ii) the dynamical heterogeneity affects the form of the master curve of the universal scaling between the structural relaxation and <u(2)>.