Frequency-dependent Stokes-Einstein relation in supercooled liquids.

We investigate by molecular dynamics simulations the validity of the frequency-dependent Stokes-Einstein (SE) relation in supercooled liquids at different temperatures. The results indicate that the SE relation holds at intermediate frequencies that correspond to the beta -relaxation and the onset of the alpha -relaxation regimes. Large deviations, which increase as the temperature decreases, are observed at frequencies well below the frequency at which the non-Gaussian parameter alpha2 is maximum. We argue that the breakdown of the SE relation in supercooled liquids arises from underestimation of the diffusion coefficient due to neglect of correlated motions.