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 simulat ions of an equilibrium glass-forming liquid, and show that long range spati al correlations of displacements emerge and grow on cooling toward the mode coupling critical temperature.