Collective dynamics of freely interacting walking droplets*

Millimetric fluid droplets may "walk" along the surface of a vibrating fluid bath, self-propelled through a resonant interaction with their own wave field. These walking droplets, or walkers, represent a classical realization of a pilot-wave system that exhibits wave-particle features previously thought to be exclusive to the quantum realm. Notably, the development of Hydrodynamic Quantum Analogs (HQAs) involving multiple walkers has been limited by the inability to prevent the droplet-droplet coalescence resulting from direct collisions between walkers. We demonstrate that increasing the ambient pressure enables the experimental investigation of freely interacting walkers by strengthening the lubrication forces between droplets, thus preventing coalescence. Moreover, our accompanying simulations of large collections of walkers reveal that wave-mediated interactions may lead to coherent collective dynamics, including the emergence of wave-like statistics in corrals. We characterize the influence of various system parameters, including corral size, memory, particle inertia, and vertical phase. Our collective system opens avenues for the study of wave-mediated active matter and exploring new hydrodynamic analogs of quantum systems, including collective dynamics in quantum condensates.