Ponderomotive Forces in Pilot-Wave Hydrodynamics

Ponderomotive effects arise in optical and acoustic systems when a particle interacts in an irregular fashion with a high-frequency field. In pilot-wave hydrodynamics, a millimetric droplet bounces on a vertically vibrating bath that accommodates a field of subharmonic Faraday waves. During a bounce, the droplet receives a horizontal `kick' whose magnitude depends on the phase of the pilot wave at impact. When droplets bounce chaotically, the direction of these kicks oscillates rapidly in time. We find that the average effect of these rapidly oscillating forces is well accounted for by a suitably defined ponderomotive force. Appealing to this ponderomotive force allows us to rationalize the behavior of a droplet walking over a standing field of Faraday waves, and the dynamics and emergent statistics of a droplet confined to a circular corral. Accompanying theoretical developments are described.