Droplets may 'walk' along the surface of a vertically vibrating fluid bath through resonant interaction with the wavefield they excite. Unlike marbles or billiard balls that interact only upon contact, the wave-mediated interactions between walking droplets give rise to a far richer spectrum of collective dynamics, including bound side-by-side propulsion, spontaneous orbiting, and statistical behaviors reminiscent of quantum particles. Until now, experimental studies of many-droplet dynamics have been hindered by coalescence during droplet-droplet collision. Here, we show that increasing ambient pressure enhances the lubrication force that resists droplet contact, thereby fully suppressing coalescence. We then confine a group of walking droplets to a circular corral within a pressurized chamber, and record their motion while they freely interact for hours without coalescence. The resulting position histogram exhibits wave-like statistics strikingly reminiscent of those observed in the quantum realm. This experimental platform opens new avenues for exploring hydrodynamic analogs of quantum many-body systems and uncovering novel phenomena in wave-mediated active matter.
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