Universal dynamics in quantum many-body systems via persistent homology

Daniel Spitz , ITP Heidelberg
Surprisingly, the dynamics of quantum systems far from equilibrium can show self-similar behavior which is the same across different physical systems and energy scales. Typically, such universal features are discussed for correlation functions. Inspired by topological data analysis techniques, we introduce persistent homology observables. 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 universal phenomena. 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 to understand far-from-equilibrium dynamics.
Cold Quantum Coffee
13 Apr 2021, 16:15
Institut für Theoretische Physik, Online

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