Persistent homology for detecting the dynamics of topological defects

Multifarious phenomena in quantum field theories are driven or accompanied by extended field configurations such as topological defects. Defects are also expected to play a prominent role for universal self-similar dynamics in systems far from equilibrium. Yet, in simulations of the paradigmatic O(N) vector model, they often appear vastly suppressed in correlations. Persistent homology can provide complementary information to correlations and reveals signatures of the different N-dependent topological defects as I will show. The Betti numbers of sublevel sets of local energy densities contain clear indications for the self-similar scaling of the defects, which has been hard to detect so far.

This application-oriented talk is based on joint work with Viktoria Noel.