Hall-Like Transverse Drift of Walking Droplets

The quantum Hall effect reveals how electrons flowing in two-dimensional systems exhibit quantized transverse conductance under strong magnetic fields, highlighting a striking departure from classical transport behavior. While some of the phenomenology of the quantum Hall effect has been realized with classical wave systems, a particle-based analog has remained elusive. Here, we demonstrate that walking droplets — macroscopic particles propelled by a resonance with their self-generated wave field — exhibit a discretized transverse drift velocity in response to the combined action of a fixed directional force, mimicking a uniform electric field, and the Coriolis force in a rotating frame, analogous to the Lorentz magnetic force. As the bath rotation rate increases, enhancing the Coriolis effect, the droplet's drift velocity evolves through a discrete sequence of steps corresponding to the quantized orbital radii that arise in the absence of directional forcing. We show that these steps are associated with the interplay between a discrete set of allowed orbits and oscillations about a preferred particle speed and orbital radius, both sustained by spatiotemporally local and nonlocal wave-mediated forces. Finally, we demonstrate that such discretized drift emerges more generically in systems where particles exhibit both a preferred speed and a discrete set of preferred orbital radii, suggesting new pathways for realizing quantized transport in classical active particle systems, and enriching the broader landscape of hydrodynamic quantum analogs.