to values around unity (corresponding to no correlations) at large $\Delta t$.

Contrasting features of cooperativity for our LCG system and that for the hard sphere systems may be interpreted as follows. In the case of hard sphere systems near the glass transition, the packing density is very high and the inter-particle interaction is a short ranged one. Therefore, the local motions of particles in hard sphere systems are naturally highly correlated in both its direction and magnitude due to the continuity constraint of particles resulting in a large scale flow with directional correlations.

In contrast, in the case of the LCG, the density of particles is relatively low ($f \simeq 0.38 $) as compared with the case of hard sphere systems near the glass transition. In addition to that, charge motions in the LCG is driven by thermal effect. From the snapshots of charge configurations, we see that there exist locally mobile regions as well as locally immobile regions. Locally immobile regions consist of charge configurations that are close to the low temperature striped patterns. Mobile regions, however, consist of charges that are agitated in random directions due to the thermal effect. Thus we do not observe positive dynamic 