Spontaneous localization of wave-dressed active particles in disordered environments

The ability of particles to move through disordered environments is central to innumerable areas, from biology and active matter to electronics. At high energies, macroscopic particles diffuse when their energy is much larger than the characteristic potential barriers of the heterogeneous landscape. By contrast, subatomic particles spontanously localize even when the disorder is weak relative to their energy — a counterintuitive phenomenon known as Anderson localization, arising from quantum wave–particle duality. Here, we present an active wave–particle system that exhibits analogous localization behavior. The system consists of millimetric droplets that self-propel across a vibrating fluid bath through resonant coupling with their own wave fields. By virtue of this coupling, these wave-dressed active particles extend classical mechanics to include features previously thought exclusive to the quantum realm. Through experiments and mathematical modeling, we investigate the erratic motion of these active particles over submerged random topographies. Ensemble statistics of their trajectories reveal spontaneous localization and suppression of diffusion when the guiding wave field spans the disordered landscape. The emergent behavior is compared with predictions from Schrödinger’s equation and interpreted in terms of a wave-mediated scattering mechanism that generates an effective potential in the long-time limit.