Spatial Correlation of the Dynamic Propensity in a Glass-Forming Liquid

We present computer simulation results on the dynamic propensity [as defined by Widmer- Cooper, Harrowell, and Fynewever, Phys. Rev. Lett. 93, 135701 (2004)] in a Kob-Andersen binary Lennard-Jones liquid system consisting of 8788 particles. We compute the spatial correlation function of the dynamic propensity as a function of both the reduced temperature T, and the time scale on which the particle displacements are measured. For T\leq0.6, we find that nonzero correlations occur at the largest length scale accessible in our system. We also show that a cluster-size analysis of particles with extremal values of the dynamic propensity, as well as 3D visualizations, reveal spatially correlated regions that approach the size of our system as T decreases, consistent with the behavior of the spatial correlation function. Next, we define and examine the "coordination propensity", the isoconfigurational average of the coordination number of the minority B particles around the majority A particles. We show that a significant correlation exists between the spatial fluctuations of the dynamic and coordination propensities. In addition, we find non-zero correlations of the coordination propensity occurring at the largest length scale accessible in our system for all T in the range 0.466<T<1.0. We discuss the implications of these results for understanding the length scales of dynamical heterogeneity in glass-forming liquids.