Non-resonant effects in pilot-wave hydrodynamics*

Pilot-wave hydrodynamics is concerned with the motion of `walkers’, millimetric droplets self-propelling on the surface of a vibrating bath, a system that has provided numerous examples of quantum-like phenomena on a macroscopic scale and so the basis for the field of hydrodynamic quantum analogs. We present a theoretical model that relaxes the assumption of resonance between the droplet and its pilot wave commonly adopted in theoretical modeling of the system. The model elucidates a number of non-resonant features of free walkers, including colinear swaying, intermittent walking, and chaotic speed oscillations linked to sporadic changes in droplet impact phase. Understanding these non-resonant effects has proven to be critical in rationalizing the emergent statistics of walkers in confined geometries and their interactions with standing Faraday waves.