Multiple time scales hidden in heterogeneous dynamics of glass-forming liquids

Abstract

A multi-time probing of density fluctuations is introduced to investigate hidden time scales of heterogeneous dynamics in glass-forming liquids. Molecular dynamics simulations for simple glass-forming liquids are performed, and a three-time correlation function is numerically calculated for general time intervals. It is demonstrated that the three-time correlation function is sensitive to the heterogeneous dynamics and that it reveals couplings of correlated motions over a wide range of time scales. Furthermore, the time scale of the heterogeneous dynamics $τ_{\rm hetero}$ is determined by the change in the second time interval in the three-time correlation function. The present results show that the time scale of the heterogeneous dynamics $τ_{\rm hetero}$ becomes larger than the $α$-relaxation time at low temperatures and large wavelengths. We also find a dynamical scaling relation between the time scale $τ_{\rm hetero}$ and the length scale $ξ$ of dynamical heterogeneity as $τ_{\rm hetero} \sim ξ^{z}$ with $z=3$.