标题： 玻璃动力学在动态模式分解中的特征 显示英文标题

标题： Signature of glassy dynamics in dynamic modes decompositions

摘要： 玻璃传统上以其无序的低能态的崎岖景观以及其缓慢趋向热力学平衡的特性来描述。 远离平衡时，也观察到了具有异常代数弛豫的动力学玻璃行为形式，例如在耦合振子网络中。 由于这些系统的无序性和高维特性，它们在理论上一直难以研究，但数据驱动的方法正在成为一种有前景的替代方法，可能有助于它们的分析。 在此，我们使用动态模态分解来表征玻璃动力学，这是一种数据驱动的谱计算方法，用于近似Koopman谱。 我们展示了在表现出代数弛豫的系统中，Koopman谱中的振荡模式和衰减模式之间的间隙消失，因此，我们提出了一种与模型无关的特征，用于稳健地检测和分析玻璃动力学。 我们通过一个一维常微分方程的最小示例和一个耦合振子的高维示例来展示我们方法的实用性。 显示英文摘要

摘要： Glasses are traditionally characterized by their rugged landscape of disordered low-energy states and their slow relaxation towards thermodynamic equilibrium. Far from equilibrium, dynamical forms of glassy behavior with anomalous algebraic relaxation have also been noted, for example, in networks of coupled oscillators. Due to their disordered and high-dimensional nature, such systems have been difficult to study theoretically, but data-driven methods are emerging as a promising alternative that may aid in their analysis. Here, we characterize glassy dynamics using the dynamic mode decomposition, a data-driven spectral computation that approximates the Koopman spectrum. We show that the gap between oscillatory and decaying modes in the Koopman spectrum vanishes in systems exhibiting algebraic relaxation, and thus, we propose a model-agnostic signature for robustly detecting and analyzing glassy dynamics. We demonstrate the utility of our approach through both a minimal example of a one-dimensional ODE and a high-dimensional example of coupled oscillators.