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We define a correlation function that quantifies the spatial correlation ofsingle-particle displacements in liquids and amorphous materials. We show foran equilibrium liquid that this function is related to fluctuations in a bulkdynamical variable. We evaluate this function using computer simulations of anequilibrium glass-forming liquid, and show that long range spatial correlationsof displacements emerge and grow on cooling toward the mode coupling criticaltemperature

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