Multi-time density correlation functions in glass-forming liquids: Probing dynamical heterogeneity and its lifetime

摘要

A multi-time extension of a density correlation function is introduced toreveal temporal information about dynamical heterogeneity in glass-formingliquids. We utilize a multi-time correlation function that is analogous to thehigher-order response function analyzed in multidimensional nonlinearspectroscopy. Here, we provide comprehensive numerical results of thefour-point, three-time density correlation function from longtime trajectoriesgenerated by molecular dynamics simulations of glass-forming binary soft-spheremixtures. We confirm that the two-dimensional representations in both time andfrequency domains are sensitive to the dynamical heterogeneity and that itreveals the couplings of correlated motions, which exist over a wide range oftime scales. The correlated motions detected by the three-time correlationfunction is divided into mobile and immobile contributions that are determinedfrom the particle displacement during the first time interval. We show that thepeak positions of the correlations are in accord with the information on thenon-Gaussian parameters of the van-Hove self correlation function. Furthermore,it is demonstrated that the progressive changes in the second time interval inthe three-time correlation function enable us to analyze how correlations indynamics evolve in time. From this analysis, we evaluated the lifetime of thedynamical heterogeneity and its temperature dependence systematically. Ourresults show that the lifetime of the dynamical heterogeneity becomes muchslower than the $\alpha$-relaxation time that is determined from the two-pointdensity correlation function when the system is highly supercooled.