Finding self-similar behavior in quantum many-body dynamics via persistent homology

Understand

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.