Excitation lines and the breakdown of Stokes-Einstein relations in supercooled liquids.

By applying the concept of dynamical facilitation and analyzing the excitation lines that result from this facilitation, we investigate the origin of decoupling of transport coefficients in supercooled liquids. We illustrate our approach with two classes of models. One depicts diffusion in a strong glass former, and the other in a fragile glass former. At low temperatures, both models exhibit violation of the Stokes-Einstein relation, D approximately tau(-1), where D is the self-diffusion constant and tau is the structural relaxation time. In the strong case, the violation is sensitive to dimensionality d, going as D approximately tau(-2/3) for d=1 and as D approximately tau(-0.95) for d=3. In the fragile case, however, we argue that dimensionality dependence is weak, and show that for d=1, D approximately tau(-0.73). This scaling for the fragile case compares favorably with the results of a recent experimental study for a three-dimensional fragile glass former.