标题： 玻璃动态特性的动力学模式分解签名 显示英文标题

标题： Signature of glassy dynamics in dynamic modes decompositions

摘要： 玻璃体传统上以其无序的低能态和缓慢向热力学平衡弛豫的崎岖景观为特征。在远离平衡状态下，也观察到了具有异常代数弛豫的动力学形式的玻璃态行为，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，这类系统在解析上一直难以研究，但数据驱动的方法作为一种有前景的替代方法正在出现，可能有助于它们的表征。在这里，我们展示了在表现出代数弛豫的系统中，库普曼谱中振荡模式和衰减模式之间的间隙消失。动态模态分解是一种数据驱动的谱计算方法，可近似库普曼谱，因此为检测和分析玻璃态动力学提供了一种模型无关的特征。我们通过一维常微分方程的一个最小例子和一个耦合振子的高维例子展示了我们的方法的实用性。 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, e.g., in networks of coupled oscillators. Due to their disordered and high-dimensional nature, such systems have been difficult to study analytically, but data-driven methods are emerging as a promising alternative that may aid in their characterization. Here, we show that the gap between oscillatory and decaying modes in the Koopman spectrum vanishes in systems exhibiting algebraic relaxation. The dynamic mode decomposition, which is a data-driven spectral computation that approximates the Koopman spectrum, thus provides a model-agnostic signature for detecting and analyzing glassy dynamics. We demonstrate the utility of our approach through both a minimal example of one-dimensional ODEs and a high-dimensional example of coupled oscillators.