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Peer-reviewedCC BY 4.0New Journal of Physics

An active Lorentz gas: walking droplets in periodic media

  • Aleksi Majaniemi1
  • Esko Toivonen1
  • Rahil Valani2
  • Rainer Klages3
  • Esa Räsänen1
  1. 1Tampere University Faculty of Engineering and Natural Sciences
  2. 2University of Oxford
  3. 3Queen Mary University of London
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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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Cite

BibTeXRIS
BibTeX
@article{majaniemi2026active,
  title = {{An active Lorentz gas: walking droplets in periodic media}},
  author = {Aleksi Majaniemi and Esko Toivonen and Rahil Valani and Rainer Klages and Esa Räsänen},
  journal = {New Journal of Physics},
  year = {2026},
  month = nov,
  doi = {10.1088/1367-2630/aebdbe},
  url = {https://iopscience.iop.org/article/10.1088/1367-2630/aebdbe},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - An active Lorentz gas: walking droplets in periodic media
AU  - Aleksi Majaniemi
AU  - Esko Toivonen
AU  - Rahil Valani
AU  - Rainer Klages
AU  - Esa Räsänen
PY  - 2026
DA  - 2026/11/04
JO  - New Journal of Physics
DO  - 10.1088/1367-2630/aebdbe
UR  - https://iopscience.iop.org/article/10.1088/1367-2630/aebdbe
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.
SN  - 1367-2630
ER  -