Probing universal dynamics with topological data analysis in a gluonic plasma

Abstract

We study nonequilibrium dynamics of SU(2) lattice gauge theory in Minkowski space-time in a classical-statistical regime, where characteristic gluon occupancies are much larger than unity. In this strongly correlated system far from equilibrium, the correlations of energy and topological densities show self-similar behavior related to a turbulent cascade towards higher momentum scales. We employ persistent homology to infer topological features of the gluonic plasma via a hierarchy of simplicial and cubical complexes. All topological observables under investigation are also manifestly gauge invariant and are shown to exhibit self-similar evolution, which relate the spatial and temporal properties of the plasma in terms of universal scaling exponents and functions. The findings may help to understand the early stages of heavy-ion collisions in the limit of high energies, and our methods can also facilitate the topological analysis of other complex systems such as encountered in experiments with ultracold quantum gases.

Constraining the initial stages of ultrarelativistic nuclear collisions

“…These studies rely on PCA, but a number of other machine learning techniques exist which may provide a more refined picture, such as Topological Data Analysis (see e.g. [173]) which has recently been explored in a somewhat related physical context [174].…”