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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 simulated data 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 universal phenomena. A possible explanation of the underlying processes is provided in terms of mixing wave turbulence and 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.
Caustics are a striking phenomena in natural optics and hydrodynamics: high-amplitude characteristic patterns that are singular in the short wavelength limit. We use exact numerical and approximate semiclassical analytic methods to study quant
Entanglement of spatial bipartitions, used to explore lattice models in condensed matter physics, may be insufficient to fully describe itinerant quantum many-body systems in the continuum. We introduce a procedure to measure the Renyi entanglement e
We study the ground state properties and nonequilibrium dynamics of two spinor bosonic impurities immersed in a one-dimensional bosonic gas upon applying an interspecies interaction quench. For the ground state of two non-interacting impurities we re
We develop a theory for light propagating in an atomic Bose-Einstein condensate in the presence of strong interactions. The resulting many-body correlations are shown to have profound effects on the optical properties of this interacting medium. For
The open dynamics of quantum many-body systems involve not only the exchange of energy, but also of other conserved quantities, such as momentum. This leads to additional decoherence, which may have a profound impact in the dynamics. Motivated by thi