that the model exhibits a separation of the two characteristic time scales, i.e., the time scale of single particle diffusion and that of structural relaxation. This feature is quite analogous to the breakdown of the SE relation observed in supercooled liquids. Stretched exponential relaxation is observed to be accompanied by interesting dynamic heterogeneity in the system. It appears that the kinetic heterogeneity is the underlying reason for both the stretched exponetial relaxation and the separation of the relaxation and diffusion time scales.

A convenient measure for dynamic heterogeneity is the so called dynamic cooperativity [@doliwa] of the particle motions. This measures reduction of the effective degrees of freedom. One interesting result from our simulations is that the magnitude of the velocity (or displacement vector) exhibits strong increase in cooperativity of the particle motions. On the other hand, the displacement vector itself shows cooperativity a little smaller than unity due to anti-correlations in the direction of particle motions. This means that the system can be divided into highly mobile regions and relatively inert regions resulting in highly inhomogeneous local mobility distribution. However, there is no macroscopic flow of particles that will generate long range positive correlations between the directions of flows 