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We study nonequilibrium dynamics of relativistic $N$-component scalar fieldtheories in Minkowski space-time in a classical-statistical regime, wheretypical occupation numbers of modes are much larger than unity. In thisstrongly correlated system far from equilibrium, the role of differentphenomena such as nonlinear wave propagation and defect dynamics remains to beclarified. We employ persistent homology to infer topological features of thenonequilibrium many-body system for different numbers of field components $N$via a hierarchy of cubical complexes. Specifically, we show that the persistenthomology of local energy density fluctuations can give rise to signatures ofself-similar scaling associated with topological defects, distinct from thescaling behaviour of nonlinear wave modes. This contributes to the systematicunderstanding of the role of topological defects for far-from-equilibrium timeevolutions of nonlinear many-body systems.

Detecting defect dynamics in relativistic field theories far from equilibrium using topological data analysis