Speaker: Javier del Pino
Affiliation: IFIMAC, Madrid
Date: Thursday, 19 February 2026 at 12:00
Location: Seminar Room, Serrano 113b
In this talk, I will present flow topology as a practical route to classify dynamical phases in driven dissipative nonlinear systems, distinct from band-topology approaches in Hermitian and non Hermitian periodic settings. The key idea is to extract global information from the semiclassical phase-space flow pattern across all initial conditions, beyond local order parameters.
Using parametrically driven nonlinear resonators as an example, I will introduce a graph-based topological invariant which captures all dynamical phase transitions as drive and detuning are varied, including both local changes, such as local instabilities, and global ones, such as how regions of initial conditions connect to different long-time behaviors. I will show how these predictions are directly confirmed experimentally in a nonlinear electromechanical resonator [1]. I will then show how flow topology also appears in the quantum steady state probability distributions and in asymmetries of their linear responses [2].
Finally, I will extend the framework to limit-cycle phases with persistent oscillations in the steady state. An extension of the graph-invariant above will capture more complex phase transitions, including mergers of limit cycles and the formation of forbidden regions in phase space. In the quantum regime, these flow-topology changes reflect dynamical phase transitions in the transient evolution, even when they are not directly reflected in standard indicators such as the Liouvillian spectral gap [3].
References
[1] Villa et al., Topological classification of driven-dissipative nonlinear systems, Sci. Adv.11, eadt9311 (2025)
[2] Seibold et al., Manifestations of flow topology in a quantum driven-dissipative system, arXiv:2508.16486 (2025).
[3] Gómez and del Pino, Quantum Dynamical Signatures of Topological Flow Transitions in Limit Cycle Phases, arXiv:2512.11747 (2025).