An active Lorentz gas: walking droplets in periodic media
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.
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BibTeX
@misc{majaniemi2026active,
title = {{An active Lorentz gas: walking droplets in periodic media}},
author = {Aleksi Majaniemi and Esko Toivonen and Rahil N. Valani and Rainer Klages and Esa Räsänen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.02419},
eprint = {2609.02419},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02419},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An active Lorentz gas: walking droplets in periodic media
AU - Aleksi Majaniemi
AU - Esko Toivonen
AU - Rahil N. Valani
AU - Rainer Klages
AU - Esa Räsänen
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2609.02419
UR - https://arxiv.org/abs/2609.02419
AB - 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.
ER -