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SYQS: Symposium Nonequilibrium Collective Behavior in Open Classical and Quantum Systems
SYQS 1: Nonequilibrium Collective Behavior in Open Classical and Quantum Systems
SYQS 1.4: Hauptvortrag
Donnerstag, 20. März 2025, 16:45–17:15, H1
Topological classification of driven-dissipative nonlinear systems — •Oded Zilberberg1, Greta Villa1, Kilian Seibold1, Vincent Dumont2, Gianluca Rastelli3, Mateusz Michałek4, Alexander Eichler2, and Javier del Pino1 — 1Department of Physics, University of Konstanz, Universitätsstraße 10, 78464 Konstanz, Germany — 2Laboratory for Solid State Physics, ETH Zurich, CH-8093 Zürich, Switzerland — 3Pitaevskii BEC Center, CNR-INO and Dipartimento di Fisica, Università di Trento, I-38123, Trento, Italy — 4Dept. of Mathematics and Statistics, University of Konstanz, Universitätsstraße 10, 78464 Konstanz, Germany
Topological classification of matter has become crucial for understanding the linear response of (meta-)materials, with associated quantized bulk phenomena and robust topological boundary effects. Moving to nonlinear systems, we develop an approach that harnesses the topology of structurally stable vector flows, and thus propose a new topological graph invariant to characterize out-of-equilibrium dynamical systems. We exemplify our approach on the ubiquitous model of a dissipative bosonic Kerr cavity, subject both to one- and two-photon drives. Using our classification, we can identify the topological origin of phase transitions in the system, as well as explain the robustness of a multicritical point in the phase diagram. We, furthermore, identify that the invariant distinguishes population inversion transitions in the system in similitude to a Z2 index. Our approach spans across the classical-to-quantum regimes, and extensions to coupled nonlinear cavities are postulated.
Keywords: Open many-body systems; Topological classification; Driven nonlinear resonators; Quantum-to-classical limit; Floquet engineering