Report on scipost_202102_00007v1
Daniel Spitz, Jürgen Berges, Markus K. Oberthaler, Anna Wienhard · 2021
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 universal 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 manybody dynamics in terms of robust topological structures beyond standard field theoretic techniques. A The mathematics of persistent homology 24A.1 Relevant notions from algebraic topology 24 A.2 The construction and structure of persistent homology groups 25 B The computational pipeline 26 C Packing relation from bounded total persistence 27 D Relating persistent homology exponents to correlation function exponents 27 E Details on the nonrelativistic Bose gas simulations 28 F 2-point correlation function results in the infrared 28 G Numerical convergence of persistent homology observables 30 H Numerical protocol to extract persistent homology scaling exponents 33 References 34