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.

中文翻译：

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通过持久同源性在量子多体动力学中寻找自相似行为

受拓扑数据分析技术的启发，我们引入了持久同源可观测量，并将它们应用于量子场论动力学的几何分析。作为原型应用，我们考虑来自远离平衡的二维 Bose 气体的经典统计模拟的数据。我们发现了动态标度指数的连续谱，它提供了非平衡自相似现象的精细分类。根据混合点云中的强波湍流和异常涡流动力学分量，提供了对潜在过程的可能解释。我们发现持久同源缩放指数与系统的几何形状有内在联系，正如包装关系的推导所揭示的那样。