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 densit y correlation function. We show that the main contribution to the correspon ding generalized susceptibility chi(4)(t) in a molecular dynamics simulatio n of a Lennard-Jones liquid arises from spatial correlations between tempor arily localized ("caged") particles. By comparing chi(4)(t) with a generali zed susceptibility chi(M)(t) related to a correlation function for the squa red particle displacements, we demonstrate a connection between dynamical h eterogeneity and the decoupling of relaxation and diffusion. (C) 2000 Ameri can Institute of Physics. [S0021-9606(00)52402-7].