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Lifetime of dynamical heterogeneity in a highly supercooled liquid

We numerically examine dynamical heterogeneity in a highly supercooled three-dimensional liquid via molecular-dynamics simulations. To define the local dynamics, we consider two time intervals, $τ_α$ and $τ_{\text{ngp}}$. $τ_α$ is the $α$ relaxation time, and $τ_{\text{ngp}}$ is the time at which non-Gaussian parameter of the van Hove self-correlation function is maximized. We determine the lifetimes of the heterogeneous dynamics in these two different time intervals, $τ_{\text{hetero}}(τ_α)$ and $τ_{\text{hetero}}(τ_{\text{ngp}})$, by calculating the time correlation function of the particle dynamics, i.e., the four-point correlation function. We find that the difference between $τ_{\text{hetero}}(τ_α)$ and $τ_{\text{hetero}}(τ_{\text{ngp}})$ increases with decreasing temperature. At low temperatures, $τ_{\text{hetero}}(τ_α)$ is considerably larger than $τ_α$, while $τ_{\text{hetero}}(τ_{\text{ngp}})$ remains comparable to $τ_α$. Thus, the lifetime of the heterogeneous dynamics depends strongly on the time interval.