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Dynamical heterogeneity in a highly supercooled liquid: Consistent calculations of correlation length, intensity, and lifetime

We have investigated dynamical heterogeneity in a highly supercooled liquid using molecular-dynamics simulations in three dimensions. Dynamical heterogeneity can be characterized by three quantities: correlation length $ξ_4$, intensity $χ_4$, and lifetime $τ_{\text{hetero}}$. We evaluated all three quantities consistently from a single order parameter. In a previous study (H. Mizuno and R. Yamamoto, Phys. Rev. E {\bf 82}, 030501(R) (2010)), we examined the lifetime $τ_{\text{hetero}}(t)$ in two time intervals $t=τ_α$ and $τ_{\text{ngp}}$, where $τ_α$ is the $α$-relaxation time and $τ_{\text{ngp}}$ is the time at which the non-Gaussian parameter of the Van Hove self-correlation function is maximized. In the present study, in addition to the lifetime $τ_{\text{hetero}}(t)$, we evaluated the correlation length $ξ_4(t)$ and the intensity $χ_4(t)$ from the same order parameter used for the lifetime $τ_{\text{hetero}}(t)$. We found that as the temperature decreases, the lifetime $τ_{\text{hetero}}(t)$ grows dramatically, whereas the correlation length $ξ_4(t)$ and the intensity $χ_4(t)$ increase slowly compared to $τ_{\text{hetero}}(t)$ or plateaus. Furthermore, we investigated the lifetime $τ_{\text{hetero}}(t)$ in more detail. We examined the time-interval dependence of the lifetime $τ_{\text{hetero}}(t)$ and found that as the time interval $t$ increases, $τ_{\text{hetero}}(t)$ monotonically becomes longer and plateaus at the relaxation time of the two-point density correlation function. At the large time intervals for which $τ_{\text{hetero}}(t)$ plateaus, the heterogeneous dynamics migrate in space with a diffusion mechanism, such as the particle density.