Universal structures far from equilibrium in alpha complexes and persistent homology.

Inspired by topological data analysis techniques, persistent homology observables are introduced in order to geometrically detect connectivity and clustering structures in quantum field theories. Serving as a prototype application, the concept of self-similarity in the vicinity of nonthermal fixed points in far-from-equilibrium quantum systems is extended to persistent homology observables. Crucially, in classical-statistical simula- tions of the two-dimensional nonrelativistic Bose gas we discover a continuous scaling exponent spectrum. A possible explanation is provided in terms of mixing strong wave turbulence and anomalous vortex kinetics components in point clouds. Persistent ho- mology scaling exponents are inherently linked to the geometry of the physical system, as the derivation of a packing relation reveals. The results given in this work demon- strate that the persistent homology machinery offers powerful and versatile methods to understand quantum systems beyond the language of correlation functions.