Time-dependent, four-point density correlation function description of dynamical heterogeneity and decoupling in supercooled liquids

Dynamical heterogeneity and the decoupling of diffusion and relaxation in a supercooled liquid is investigated via a time-dependent, four-point density correlation function. We show that the main contribution to the corresponding generalized susceptibility x4(t) in a molecular dynamics simulation of a Lennard-Jones liquid arises from spatial correlations between temporarily localized ~‘‘caged’’! particles. By comparing x4(t) with a generalized susceptibility xM(t) related to a correlation function for the squared particle displacements, we demonstrate a connection between dynamical heterogeneity and the decoupling of relaxation and diffusion. © 2000 American Institute of Physics. @S0021-9606~00!52402-7#