An active Lorentz gas: walking droplets in periodic media

Journal article

Abstract The Lorentz gas is a paradigmatic model in dynamical systems theory for understanding the origin of nonequilibrium transport in terms of microscopic deterministic chaos. In the periodic setting, a point particle scatters elastically off disks arranged on a two-dimensional lattice. Here we replace the disks by smooth potentials and the particle by the widely studied walking droplet, which propels itself on a vertically vibrating fluid. In the low-memory limit, this droplet reduces to a particle with nonlinear active friction. We call this system an active Lorentz gas. Using extensive numerical simulations, we analyze how dissipation generated by the active deterministic dynamics alters the phase-space structure of the corresponding conservative Lorentz gas. We find that islands of stability collapse into attracting and repelling sets. To characterize these structures, we introduce an energy-variance filtering method that distinguishes localized periodic, quasi-ballistic periodic, and chaotic trajectories, enabling the construction of bifurcation diagrams in a non-conservative setting. We identify parameter regimes exhibiting strong bifurcation cascades, anomalous diffusion, and significant phase-space contraction. Our results establish the active Lorentz gas as a rich framework for studying transport in dissipative dynamical systems and provide a bridge between active matter and classical models of chaotic transport, with potential implications for hydrodynamic quantum analogs in periodic media.

Authors: Majaniemi, A; Toivonen, E; Valani, R; Klages, R; Räsänen, E

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: IOP Publishing
• Journal: New Journal of Physics More from this journal
• Volume: 28
• Issue: 11
• Publication date: 2026-11-04
• DOI: 10.1088/1367-2630/aebdbe
• EISSN: 1367-2630
• ISSN: 1367-2630
• Language: English
• Keywords: periodic media; phase space contraction; dissipative dynamical systems; bifurcation cascade; Lorentz gas; deterministic chaos; active matter; walking droplets; anomalous diffusion; nonequilibrium transport