Multi-time correlation analysis for heterogeneous dynamics in glass-forming liquids

引入了密度关联函数的多时间扩展，以揭示玻璃形成液体中动力学非均质性的时间信息。研究中使用的多时间相关函数类似于多维非线性光谱学中分析的高阶响应函数。我们证实了二维表示对动力学不均匀是敏感的，并且揭示了存在于广泛时间尺度上的相关运动的耦合。通过这一分析，我们系统地评估了动力学非均匀态的寿命及其与温度的关系。此外，我们还考察了动力学非均匀寿命在破坏粘性和自扩散常数之间的斯托克斯-爱因斯坦(SE)关系中的物理作用。严重违反SE关系的特征是时间尺度长于高过冷液体中动力学不均匀的寿命。

A multi-time extension of a density correlation function is introduced to reveal temporal information about dynamical heterogeneity in glass-forming liquids. A multi-time correlation function utilized in this study is analogous to the higher-order response function analyzed in multidimensional nonlinear spectroscopy. We confirm that the two-dimensional representations are sensitive to the dynamical heterogeneity and that these reveal the couplings of correlated motions, which exist over a wide range of time scales. From this analysis, we evaluated the lifetime of the dynamical heterogeneity and its temperature dependence systematically. Furthermore, we examine the physical role of the lifetime of dynamical heterogeneity in the violation of the Stokes-Einstein (SE) relation between viscosity and self-diffusion constant. Large violations of the SE relation are characterized by time scales longer than the lifetime of the dynamical heterogeneity in highly supercooled liquids.