Collective Dynamics of Walking Droplets: Towards a Hydrodynamic Analog of Quantum Condensates

Millimetric droplets may "walk" along the surface of a vibrating fluid bath, self-propelled through a resonant interaction with the waves they generate upon each bounce. Here, we investigate the collective dynamics of many such “walkers” confined within a circular corral. We demonstrate that wave-mediated interactions drive a transition from an uncoupled, gas-like state to a coherent, global wave state in a manner reminiscent of quantum condensates approaching absolute zero. We systematically sweep the parameter space to characterize this collective transition in terms of corral size, particle packing and inertia, path memory, and pilot-wave extent. Notably, we also observe a resonance between corral size and this global wave state, which reappears periodically with increasing corral radius. Special attention is given to elucidating the mechanisms underlying both the emergence of the global wave state and its resonance with corral size. As the bath’s vertical forcing increases, the effective size of the wave packet produced by each walker grows, eventually saturating the domain and coupling the dynamics of all walkers through a system-wide mean wave potential. The associated corral-size resonance arises from the interference pattern generated by local wave contributions over a disc. We conclude by discussing the experimental realization of such wave-mediated collective dynamics, which has thus far been hindered by droplet-droplet coalescence and desynchronization of their vertical bouncing phases. This collective walker framework opens new avenues for exploring wave-mediated active matter and developing hydrodynamic analogs of quantum many-body phenomena, including quantum condensates, many-body localization, and Hall phases.