论文标题
路径积分方法揭示了复杂能量景观在玻璃系统激活动力学方面的作用
Path Integral Approach Unveils the Role of Complex Energy Landscape for Activated Dynamics of Glassy Systems
论文作者
论文摘要
越来越多的系统的复杂动力学归因于具有指数数量的亚稳态状态的崎and能量景观的出现。要将这张图片发展为预测的动力学理论，我讨论了如何计算从一个亚稳态到另一个状态的跳跃的指数较小的概率。这被表示为一个路径积分，可以通过平均场模型中的鞍点方法评估，从而导致边界值问题。所得的动态方程是通过范式球形$ P $ - SPIN玻璃模型中的Newton-Krylov算法进行数值求解的，该玻璃模型在从过冷液体到机器学习算法的各种环境中被调用。我讨论了大时代的渐近状态中的解决方案，以及对成真性过程性质的物理意义。
The complex dynamics of an increasing number of systems is attributed to the emergence of a rugged energy landscape with an exponential number of metastable states. To develop this picture into a predictive dynamical theory I discuss how to compute the exponentially small probability of a jump from one metastable state to another. This is expressed as a path integral that can be evaluated by saddle-point methods in mean-field models, leading to a boundary value problem. The resulting dynamical equations are solved numerically by means of a Newton-Krylov algorithm in the paradigmatic spherical $p$-spin glass model that is invoked in diverse contexts from supercooled liquids to machine-learning algorithms. I discuss the solutions in the asymptotic regime of large times and the physical implications on the nature of the ergodicity-restoring processes.
