Time-dependent four-point density correlation functions in supercooled liquids

Abstract

Dynamical heterogeneity and the decoupling of diffusion and structural relaxation in a supercooled liquid is investigated in terms of a time-dependent, fourth-order density correlation function. The generalized susceptibility ${\chi }_4(t)$ corresponding to this correlation function has a maximum at an intermediate time $t_4^{\ast }$, and both $t_4^{\ast }$ and ${\chi }_4(t_4^{\ast })$ grow strongly with decreasing temperature. We show that the main contribution to ${\chi }_4(t)$ arises from spatial correlations between temporarily localized (``caged'') particles. We compare ${\chi }_4(t)$ with a generalized susceptibility ${\chi }_M(t)$ related to a correlation function of squared particle displacements, and show that while $t_4^{\ast }$ is roughly proportional to the $\alpha$-relaxation time, $t_M^{\ast }$ is proportional to the inverse of the self-diffusion coefficient.

References updated. Inset added to Figure 3