论文标题
重新访问超冷液体的$β$ - 递延的单砂模型
Revisiting the single-saddle model for the $β$-relaxation of supercooled liquids
论文作者
论文摘要
玻璃形成液体的动力学表现出几个出色的特征，例如两步松弛和动态异质性，这些功能很难从第一原理中进行定量预测。在这项工作中，我们重新审视了$β$ - 递延的简单理论模型，即放松动力学的第一步。该模型首先由Cavagna等人引入，描述了势能表面鞍点附近系统的动力学。我们扩展了模型以说明密度密度相关函数和4点动态敏感性。我们获得了一个简单的示意图模型的分析结果，与P-Spin模型的相关结果以及不均匀模式耦合理论的预测接触。在最近的计算进步的基础上，我们还明确地将模型预测与靠近模式耦合交叉的玻璃形成液体的过度阻尼的Langevin动力学模拟进行了比较。该协议仅在单粒子动态特性的水平上进行定量，直到早期$β$ - 政权。但是，由于其固有的谐波近似，该模型无法预测与结构放松相关的时间尺度上的动力学。但是，我们的分析表明，如果正确考虑了模式的空间定位，与模拟的协议可能会在很大程度上得到改善。
The dynamics of glass-forming liquids display several outstanding features, such as two-step relaxation and dynamic heterogeneities, which are difficult to predict quantitatively from first principles. In this work, we revisit a simple theoretical model of the $β$-relaxation, i.e., the first step of the relaxation dynamics. The model, first introduced by Cavagna et al., describes the dynamics of the system in the neighborhood of a saddle point of the potential energy surface. We extend the model to account for density-density correlation functions and for the 4-point dynamic susceptibility. We obtain analytical results for a simple schematic model, making contact with related results for p-spin models and with the predictions of inhomogeneous mode-coupling theory. Building on recent computational advances, we also explicitly compare the model predictions against overdamped Langevin dynamics simulations of a glass-forming liquid close to the mode-coupling crossover. The agreement is quantitative at the level of single-particle dynamic properties only up to the early $β$-regime. Due to its inherent harmonic approximation, however, the model is unable to predict the dynamics on the time scale relevant for structural relaxation. Nonetheless, our analysis suggests that the agreement with the simulations may be largely improved if the modes' spatial localization is properly taken into account.
