Far-from-equilibrium dynamics of SU (2) gauge theory with Wilson fermions is studied in 1 + 1 space-time dimensions using a real-time lattice approach. Lattice improved Hamiltonians are shown to be very efficient in simulating Schwinger pair creation and emergent phenomena such as plasma oscillations. As a consequence, significantly smaller lattices can be employed to approach continuum physics in the infinite-volume limit as compared to unimproved implementations. This allows us to compute also higher-order correlation functions including four fermion fields, which give unprecedented insights into the real-time dynamics of the fragmentation process of strings between fermions and antifermions.

Inspired by topological data analysis techniques, we introduce persistent homology observables and apply them in a geometric analysis of the dynamics of quantum field theories. As a prototype application, we consider data from a classical-statistical simulation of a two-dimensional Bose gas far from equilibrium. We discover a continuous spectrum of dynamical scaling exponents, which provides a refined classification of nonequilibrium self-similar phenomena. A possible explanation of the underlying processes is provided in terms of mixing strong wave turbulence and anomalous vortex kinetics components in point clouds. We find that the persistent homology scaling exponents are inherently linked to the geometry of the system, as the derivation of a packing relation reveals. The approach opens new ways of analyzing quantum many-body dynamics in terms of robust topological structures beyond standard field theoretic techniques.

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In einer Supraflüssigkeit können sich Anregungen ohne Reibung ausbreiten, wie man anhand von Wolken aus ultrakalten Atomen hervorragend studieren kann. In unseren Experimenten in Heidelberg ist es uns gelungen, zum ersten Mal die Koexistenz zweier sehr unterschiedlicher Supraflüssigkeiten zu realisieren und mittels neuartiger Methoden die Struktur dieser besonderen Quantenmaterie zu untersuchen.