Anderson Localization of Walking Droplets

Abstract: Understanding the ability of particles to move in disordered environments is a central problem in innumerable settings, from biology and active matter to electronics. Macroscopic particles in disordered environments ultimately exhibit diffusive motion when their energy exceeds the characteristic potential barrier of the heterogeneous background. In contrast, subatomic particles in random media come to rest even when the disorder is weak, an intriguing phenomenon known as Anderson localization caused by the quantum wave-particle duality. In this talk, we present a hydrodynamic wave-particle system whose dynamics exhibit localized statistics analogous to those of quantum particles. The constituents of our hydrodynamic system are millimetric liquid droplets that walk across the surface of a vibrating fluid bath, self-propelled through a resonant interaction with their own wave fields. By virtue of the coupling with their wave fields, these walking droplets, or 'walkers', exhibit certain features previously thought to be exclusive to the subatomic, quantum realm. Through experiments and mathematical modeling, we investigate the erratic motion of walkers over submerged random topographies. Consideration of an ensemble of walker trajectories reveals localized particle statistics and an absence of diffusion when the wave field extends over the disordered topography. The emergent statistics are compared to predictions from Schrödinger's equation, and rationalized in terms of a wave-mediated scattering mechanism, which generates an effective potential in the long-time limit.