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

Abstract

We study nonequilibrium dynamics of relativistic $N$-component scalar field theories in Minkowski space-time in a classical-statistical regime, where typical occupation numbers of modes are much larger than unity. In this strongly correlated system far from equilibrium, the role of different phenomena such as nonlinear wave propagation and defect dynamics remains to be clarified. We employ persistent homology to infer topological features of the nonequilibrium many-body system for different numbers of field components $N$ via a hierarchy of cubical complexes. Specifically, we show that the persistent homology of local energy density fluctuations can give rise to signatures of self-similar scaling associated with topological defects, distinct from the scaling behaviour of nonlinear wave modes. This contributes to the systematic understanding of the role of topological defects for far-from-equilibrium time evolutions of nonlinear many-body systems.

arXiv comment17 pages, 9 figures

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• Condensation and prescaling in spatial Polyakov loop correlations far from equilibrium
• Topological Data Analysis of Monopole Current Networks in $U(1)$ Lattice Gauge Theory
• Anomalous non-thermal fixed point in a quasi-two-dimensional dipolar Bose gas
• Topological data analysis of the deconfinement transition in SU(3) lattice gauge theory
• Decaying superfluid turbulence near an anomalous non-thermal fixed point