Cooperativity and spatial correlations near the glass transition: Computersimulation results for hard spheres and disks

We examine the dynamics of hard spheres and disks at high packing fractions in two and three dimensions, modeling the simplest systems exhibiting a gl ass transition. As it is well known, cooperativity and dynamic heterogeneit y arise as central features when approaching the glass transition from the liquid phase, so an understanding of their underlying physics is of great i nterest. Cooperativity implies a reduction of the effective degrees of free dom, and we demonstrate a simple way of quantification in terms of the stre ngth and the length scale of dynamic correlations among different particles . These correlations are obtained for different dynamical quantities X-i(t) that an constructed from single-particle displacements during some observa tion time t. Of particular interest is the dependence on t. Interestingly, for appropriately chosen X-i(t) we obtain finite cooperativity in the limit t-->infinity.