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 ${\tau }_{\mathrm{hetero}}$ 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 ${\tau }_{\mathrm{hetero}}$ becomes larger than the $\alpha$-relaxation time at low temperatures and large wavelengths. We also find a dynamical scaling relation between the time scale ${\tau }_{\mathrm{hetero}}$ and the length scale $\xi$ of dynamical heterogeneity as ${\tau }_{\mathrm{hetero}}\sim {\xi }^z$ with $z=3$.

arXiv comment4 pages, 5 figures, to appear in Phys. Rev. E (Rapid Communications)

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