过冷液体的$β$ -松弛的单鞍模型的再讨论
Revisiting the single-saddle model for the $β$-relaxation of supercooled liquids
摘要：
玻璃形成液体的动力学表现出一些突出的特点，如两步弛豫和动态非均匀性，这是很难定量预测的第一性原理。在这项工作中，我们重新审视了一个简单的理论模型的$β$ -松弛，即，松弛动力学的第一步。该模型首先由Cavagna等人提出，描述了系统在势能面鞍点附近的动力学。我们扩展了该模型，占密度密度关联函数和4点动态磁化率。我们得到了一个简单的示意性模型的分析结果，与相关的p-自旋模型的结果和非均匀模式耦合理论的预测。建立在最近的计算进展，我们还明确比较过阻尼Langevin动力学模拟的玻璃形成液体接近模式耦合交叉的模型预测。该协议是定量的单粒子动力学性质的水平，只有到早期的$β$制度。然而，由于其固有的谐波近似，该模型是无法预测的时间尺度上的结构弛豫相关的动态。尽管如此，我们的分析表明，与模拟的协议可能会大大提高，如果模式的空间定位是适当考虑。
英文摘要：
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.
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