Topological classification of driven-dissipative nonlinear systems

Year: 2025

Authors: Villa G., Del Pino J., Dumont V., Rastelli G., Michalek M., Eichler A., Zilberberg O.

Autors Affiliation: Univ Konstanz, Dept Phys, D-78464 Constance, Germany; Swiss Fed Inst Technol, Lab Solid State Phys, CH-8093 Zurich, Switzerland; Swiss Fed Inst Technol, Quantum Ctr, CH-8093 Zurich, Switzerland; Univ Trento, Pitaevskii BEC Ctr, CNR, INO, I-38123 Trento, Italy; Univ Trento, Dipartimento Fis, I-38123 Trento, Italy; INFN, Trento Inst Fundamental Phys & Applicat, TIFPA, Via Sommar 14, I-38123 Trento, Italy; Univ Konstanz, Dept Math & Stat, D-78457 Constance, Germany.

Abstract: In topology, averaging over local geometrical details reveals robust global features. These are crucial in physics for understanding quantized bulk transport and exotic boundary effects of linear wave propagation in (meta-)materials. Beyond linear Hamiltonian systems, topological physics strives to characterize open (non-Hermitian) and interacting systems. Here, we establish a framework for the topological classification of driven-dissipative nonlinear systems by defining a graph index for their Floquet semiclassical equations of motion. Our index builds upon the topology of vector flows and encodes the particle-hole nature of excitations around all out-of-equilibrium stationary states. Thus, we uncover the topology of nonlinear resonator’s dynamics under external and parametric forcing. Our framework sheds light on the topology of driven-dissipative phases, including under- to overdamped responses and symmetry-broken phases linked to population inversion. We therefore expose the pervasive link between topology and nonlinear dynamics, with broad implications for interacting topological insulators, topological solitons, neuromorphic networks, and bosonic codes.

Journal/Review: SCIENCE ADVANCES

Volume: 11 (33)      Pages from: eadt9311-1  to: eadt9311-10

More Information: V.D. acknowledges support from ETH Zurich via Postdoctoral Fellowship grant 23-1 FEL-023. A.E. and O.Z. acknowledge support from the Swiss National Science Foundation (SNSF) through Sinergia grant CRSII5_206008/1.O.Z. also acknowledges support from the Deutsche Forschungsgemeinschaft (DFG), projects 449653034 and SFB1432; M.M. from DFG project 467575307. G.R. acknowledges support from the Provincia Autonoma di Trento (PAT).
KeyWords: Dynamics; Equations of motion; Hamiltonians; Nonlinear equations; Nonlinear simulations; Quantum theory; Topological insulators; Topology; Wave propagation
DOI: 10.1126/sciadv.adt9311