Pilot-Wave Hydrodynamics Beyond Resonance

Pilot-wave hydrodynamics provides a striking example of an active particle: a millimetric droplet that self-propels across the surface of a vibrating liquid bath through a resonant interaction with its own wave field. In this talk, I will present recent theoretical and experimental results that elucidate the role of non-resonant dynamics and phase degeneracy in walker behavior. I will first introduce a theoretical model that relaxes the assumption of strict resonance between the droplet and its pilot wave, offering new insight into intermittent walking, collinear swaying, and impact-phase switching. I will then describe a hydrodynamic analog of the Kapitza–Dirac effect, in which walking droplets are deflected by a standing Faraday wave, producing diffraction-like statistics governed by phase-dependent, non-resonant interactions. Finally, I will show how phase degeneracy can be actively controlled using multi-frequency forcing, leading to phase switching and reconfiguration of droplet lattices. Together, these studies highlight how phase dynamics and non-resonant effects shape the emergent behavior of walking droplets.