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arXiv 1004.2380cond-mat.soft
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玻璃形成液体中多时间密度关联函数:探索动力学不均匀性及其寿命

Multi-time density correlation functions in glass-forming liquids: Probing dynamical heterogeneity and its lifetime

Kang Kim, Shinji Saito

摘要:

引入了密度关联函数的多时间扩展,以揭示玻璃形成液体动力学不均匀性的时间信息。我们利用一个多时间的关联函数,这是类似于在多维非线性光谱分析的高阶响应函数。在这里,我们提供了全面的四点,三次密度关联函数从长时间的轨迹所产生的分子动力学模拟的玻璃形成二元软球混合物的数值结果。我们确认,在时间和频率域的二维表示是敏感的动力学异质性,它揭示了相关的运动,存在于广泛的时间尺度的耦合。由三次关联函数检测到的相关运动被分为移动和不移动的贡献,这是确定从粒子位移在第一时间间隔。我们发现,相关峰的位置与van-Hove自关联函数的非高斯参数信息相一致。此外,它表明,在第二个时间间隔的三次关联函数的渐进变化,使我们能够分析如何在动力学的相关性演变的时间。从这个分析中,我们评估的动力学异质性的寿命和它的温度依赖性系统。我们的研究结果表明,动力学不均匀性的寿命变得比$α$ -弛豫时间,这是确定从两点密度关联函数时,系统是高度过冷慢得多。

英文摘要:

A multi-time extension of a density correlation function is introduced to reveal temporal information about dynamical heterogeneity in glass-forming liquids. We utilize a multi-time correlation function that is analogous to the higher-order response function analyzed in multidimensional nonlinear spectroscopy. Here, we provide comprehensive numerical results of the four-point, three-time density correlation function from longtime trajectories generated by molecular dynamics simulations of glass-forming binary soft-sphere mixtures. We confirm that the two-dimensional representations in both time and frequency domains are sensitive to the dynamical heterogeneity and that it reveals the couplings of correlated motions, which exist over a wide range of time scales. The correlated motions detected by the three-time correlation function is divided into mobile and immobile contributions that are determined from the particle displacement during the first time interval. We show that the peak positions of the correlations are in accord with the information on the non-Gaussian parameters of the van-Hove self correlation function. Furthermore, it is demonstrated that the progressive changes in the second time interval in the three-time correlation function enable us to analyze how correlations in dynamics evolve in time. From this analysis, we evaluated the lifetime of the dynamical heterogeneity and its temperature dependence systematically. Our results show that the lifetime of the dynamical heterogeneity becomes much slower than the $α$-relaxation time that is determined from the two-point density correlation function when the system is highly supercooled.

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