  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.
