Classical Wave-Particle Analog of Anderson Localization (2023)
Undergraduate: Abel Abraham
Faculty Advisor: Pedro Saenz
Department: Mathematics
Understanding the ability of particles to move in disordered environments is a central problem in innumerable settings, from biology to active matter and electronics. Macroscopic particles guided by local forces ultimately exhibit diffusive motion when their energy exceeds the characteristic potential barrier of the random background. In stark contrast, subatomic particles in disordered media may become localized even when the disorder is weak, a phenomenon known as Anderson localization caused by the quantum wave-particle duality. Here, we present a classical wave-particle system in which the particles become localized like waves over random submerged topographies. 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’, extend the range of classical mechanics to include certain features previously thought to be exclusive to the microscopic, 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. Particular attention is given to characterizing the influence of the submerged topography on the emergent particle dynamics and long-time probability distributions. The localized statistics are compared to predictions from Schrödinger’s equation in the Anderson regime, and rationalized in terms of a wave-mediated scattering mechanism. This classical wave-particle analog suggests new directions for future research in various areas, including topological matter and wave localization.
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