Coslovich Daniele, Ikeda Atsushi
Dipartimento di Fisica, Università di Trieste, Strada Costiera 11, 34151 Trieste, Italy.
Graduate School of Arts and Science, University of Tokyo, Komaba, Tokyo 153-8902, Japan.
J Chem Phys. 2022 Mar 7;156(9):094503. doi: 10.1063/5.0083173.
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. [J. Phys. A: Math. Gen. 36, 10721 (2003)], 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 four-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.
玻璃形成液体的动力学表现出几个显著特征，例如两步弛豫和动态非均匀性，这些特征很难从第一性原理进行定量预测。在这项工作中，我们重新审视了β弛豫（即弛豫动力学的第一步）的一个简单理论模型。该模型最初由卡瓦尼亚等人 [《物理学报A：数学物理》36, 10721 (2003)] 提出，描述了势能面鞍点附近系统的动力学。我们扩展该模型以考虑密度 - 密度关联函数和四点动态磁化率。对于一个简单的示意模型，我们得到了解析结果，与p自旋模型的相关结果以及非均匀模耦合理论的预测建立了联系。基于近期的计算进展，我们还将模型预测与接近模耦合交叉点的玻璃形成液体的过阻尼朗之万动力学模拟进行了明确比较。仅在早期β区域，单粒子动态性质层面的一致性是定量的。然而，由于其固有的谐波近似，该模型无法预测与结构弛豫相关时间尺度上的动力学。尽管如此，我们的分析表明，如果适当地考虑模式的空间局域化，与模拟的一致性可能会大大提高。
