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 chi(4)(t) in a molecular dynamics simulation of a Lennard-Jones liquid arises from spatial correlations between temporarily localized (caged) particles. By comparing chi(4)(t) with a generalized susceptibility chi(M)(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. (C) 2000 American Institute of Physics. [S0021-9606(00)52402-7].