Stochastic approach to glass transitions

本研究项目的主要主题是阐明玻璃化转变附近的过冷液体的动力学性质，将lie俘获扩散模型应用于过冷液体中原子的随机动力学。我们设计了一种基于非高斯参数的峰值位置来定位玻璃化转变点的有效方法。与其他方法相比，这种方法功能强大，因为前者仅在有限时间内使用信息。我们用这种方法来固定软球液体的玻璃化过渡点。为了验证模型的有效性，并将模型与软球系统进行比较，研究了等待时间分布函数，推导了模型中参数与软球系统之间的显式关系。我们还研究了有限观测时间的影响。我们表明，由于次反常扩散，在达到玻璃化转变点之前，在给定精度内确定物理量所需的时间增加。我们还研究了中间散射函数和动态结构因子，并表明捕获扩散的亚异常状态产生了α弛豫的特征，其中动态结构作为频率的函数以幂律形式减小，或者中间散射函数随时间呈指数级衰减。

The main theme of the research project is to elucidate the dynamical properties of supercooled liquids near the glass transition, applying tlie trapping diffusion model to the stochastic dynamics of atoms seen in the supercooled liquids. We devised an efficient method to locate the glass transition point on the basis of the peak position of the non-Gaussian parameter. This method is powerful compared to the other methods, since the former uses only the informations at finite times. We used this method to fix the glass transition point for the soft-sphere liquid. In order to test the validity of the present model and compare the model with the softsphere system, we studied the waiting time distribution function and derived the explicit relation between the parameter in the model and the softsphere systems. We also studied the effect of the finite observation time. We showed that due to the subanomalous diffusion, the time required for the determination of physical quantities within a given accuracy increases before the glass transition point is reached. We also investigated the intermediate scattering function and the dynaurical structure factor and showed that the subanomalous regime of the trapping diffusion yields the characteristics of the alpha-relaxation, where the dynamical structure fac'Lor as a function of frequency decreases in a power-law form or the intermediate scattering function decreases stretched-exponentially in time.