论文标题
通过持续的同源性在量子多体动力学中找到自相似的行为
Finding self-similar behavior in quantum many-body dynamics via persistent homology
论文作者
论文摘要
受拓扑数据分析技术的启发，我们介绍了持久的同源性可观察物，并将其应用于量子场理论动力学的几何分析中。作为原型应用，我们考虑了来自二维bose气体远离平衡的经典统计模拟数据。我们发现了连续的动态缩放指数，该指数提供了非平衡自相似现象的精制分类。在点云中混合强波湍流和异常涡流动力学组件的角度，提供了基础过程的可能解释。我们发现，持续的同源缩放指数本质上与系统的几何形状链接，因为包装关系的推导揭示了。该方法开辟了新的方法，分析量子多体动力学，以稳健的拓扑结构超出标准场理论技术。
Inspired by topological data analysis techniques, we introduce persistent homology observables and apply them in a geometric analysis of the dynamics of quantum field theories. As a prototype application, we consider data from a classical-statistical simulation of a two-dimensional Bose gas far from equilibrium. We discover a continuous spectrum of dynamical scaling exponents, which provides a refined classification of nonequilibrium self-similar phenomena. A possible explanation of the underlying processes is provided in terms of mixing strong wave turbulence and anomalous vortex kinetics components in point clouds. We find that the persistent homology scaling exponents are inherently linked to the geometry of the system, as the derivation of a packing relation reveals. The approach opens new ways of analyzing quantum many-body dynamics in terms of robust topological structures beyond standard field theoretic techniques.
