Dresden 2026 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 8: Nonlinear Dynamics, Synchronization, and Chaos

DY 8.7: Vortrag

Montag, 9. März 2026, 11:30–11:45, ZEU/0118

Transient Signatures of Flow-Topological Transitions in Nonlinear Quantum Oscillators — •Alejandro S. Gómez and Javier del Pino — Department of Theoretical Condensed Matter Physics, (IFIMAC), Universidad Autónoma de Madrid

Non-equilibrium phases in driven-dissipative systems are ubiquitous. Often, they appear as classical fixed point attractors and limit cycles, with standard phase transitions triggered by local instabilities. Yet the flow-topology framework [1] shows that transitions can also arise from nonlocal reorganizations, leaving attractors unchanged and emerging only in transients. Stationary quantum states still reflect these structures as probability hotspots, and local changes can induce Liouvillian spectral degeneracies. However, how the nonlocal, transient reorganizations manifest in the Liouvillian remains open.

In this talk, I will introduce a topological framework that extends the classification of fixed points [1] to capture the full phase-space connectivity considering also limit cycles. By linking open quantum dynamics to the classification of Morse-Smale flows [2], Crucially, we demonstrate that our graph invariant exposes transitions the Liouvillian spectrum misses altogether, related to global flow-topology transitions. I illustrate this framework by mapping the dissipative phases of a two-photon-driven Kerr resonator with added gain.

[1] G. Villa et al., Topological classification of driven-dissipative nonlinear systems, Sci. Adv. (2025).

[2] A. A. Oshemkov, Classification of Morse-Smale flows on two-dimensional manifolds, Sbornik Math. (1998).

Keywords: Topological classification; Driven-dissipative systems; Liouvillian dynamics; Limit cycles; Global bifurcations