Growing Spatial Correlations of Particle Displacements in a Simulated Liquid on Cooling toward the Glass Transition

We define a correlation function that quantifies the spatial correlation of single-particle displacements in liquids and amorphous materials. We show that for an equilibrium liquid this function is related to fluctuations in a bulk dynamical variable. We evaluate this function using computer simulations of an equilibrium glass-forming liquid, and show that long range spatial correlations of displacements emerge and grow on cooling toward the mode coupling critical temperature. [S0031-9007(99)09452-1]