## Distribution of Diffusion Constants and Stokes-Einstein Violation in supercooled liquids    [PDF]

It is widely believed that the breakdown of the Stokes-Einstein relation between the translational diffusivity and the shear viscosity in supercooled liquids is due to the development of dynamic heterogeneity i.e. the presence of both slow and fast moving particles in the system. In this study we \emph{directly} calculate the distribution of the diffusion constant for a model system for different temperatures in the supercooled regime. We find that with decreasing temperature, the distribution evolves from Gaussian to bimodal indicating that on the time scale of the $\alpha$ relaxation time, mobile (liquid like) and less mobile (solid like) particles in the system can be \emph{unambiguously} identified. We also show that less mobile particles obey the Stokes-Einstein relation even in the supercooled regime and it is the mobile particles which show strong violation of the Stokes-Einstein relation. Finally, we show that the degree of violation of the Stokes-Einstein relation can be tuned by introducing randomly pinned particles in the system.