Uploaded October 2024 | Updated September 2026, 1 week ago
Supplementary Video 1. Walking droplet over a submerged random topography. Experimental visualization of a walking droplet moving erratically due to a submerged topography composed of tiles each with a random height above the base depth. After a sufficiently long period of time, the droplets position histogram exhibits a localization region in the top-right corner of the experimental domain.
Supplementary Video 2. Absence of diffusion. Simulations illustrating the absence of diffusion of an electron in a weak, disordered potential, and the analogous effect observed with walking droplets at high memory. At low memory, walking droplets exhibit diffusive motion.
Supplementary Video 3. Wave-mediated non-local interactions. Experiments demonstrate that, in the absence of the droplet, the Faraday waves emanate from the localization region. Below the Faraday threshold, the walking droplet resonates with the most unstable Faraday mode leading to the emergence of long-range beams that pull the droplet into the localization region. Once inside the localization region, large-amplitude waves make the droplet execute loops, increasing the trapping time. Similar wave-mediated interactions are observed in simulations.
Abstract
Understanding the ability of particles to maneuver through disordered environments is a central problem in innumerable settings, from active matter and biology to electronics. Macroscopic particles ultimately exhibit diffusive motion when their energy exceeds the characteristic potential barrier of the random landscape. In stark contrast, wave-particle duality causes electrons in disordered media to come to rest even when the potential is weak—a remarkable phenomenon known as Anderson localization. Here, we present a hydrodynamic active system with wave-particle features, a millimetric droplet self-guided by its own wave field over a submerged random topography, whose dynamics exhibits localized statistics analogous to those of electronic systems. Consideration of an ensemble of particle trajectories reveals a suppression of diffusion when the guiding wave field extends over the disordered topography. We rationalize mechanistically the emergent statistics by virtue of the wave-mediated resonant coupling between the droplet and topography, which produces an attractive wave potential about the localization region. This hydrodynamic analog, which demonstrates how a classical particle may localize like a wave, suggests new directions for future research in various areas, including active matter, wave localization, many-body localization, and topological matter.
Abel J. Abraham, Stepan Malkov, Frane A. Ljubetic, Matthew Durey, and Pedro J. Sáenz. Phys. Rev. X 14, 031047 – Published 17 September 2024
DOI:10.1103/PhysRevX.14.031047
Supplementary Video 1. Walking droplet over a submerged random topography. Experimental visualization of a walking droplet moving erratically due to a submerged topography composed of tiles each with a random height above the base depth. After a sufficiently long period of time, the droplets position histogram exhibits a localization region in the top-right corner of the experimental domain.
Supplementary Video 2. Absence of diffusion. Simulations illustrating the absence of diffusion of an electron in a weak, disordered potential, and the analogous effect observed with walking droplets at high memory. At low memory, walking droplets exhibit diffusive motion.
Supplementary Video 3. Wave-mediated non-local interactions. Experiments demonstrate that, in the absence of the droplet, the Faraday waves emanate from the localization region. Below the Faraday threshold, the walking droplet resonates with the most unstable Faraday mode leading to the emergence of long-range beams that pull the droplet into the localization region. Once inside the localization region, large-amplitude waves make the droplet execute loops, increasing the trapping time. Similar wave-mediated interactions are observed in simulations.
Abstract
Understanding the ability of particles to maneuver through disordered environments is a central problem in innumerable settings, from active matter and biology to electronics. Macroscopic particles ultimately exhibit diffusive motion when their energy exceeds the characteristic potential barrier of the random landscape. In stark contrast, wave-particle duality causes electrons in disordered media to come to rest even when the potential is weak—a remarkable phenomenon known as Anderson localization. Here, we present a hydrodynamic active system with wave-particle features, a millimetric droplet self-guided by its own wave field over a submerged random topography, whose dynamics exhibits localized statistics analogous to those of electronic systems. Consideration of an ensemble of particle trajectories reveals a suppression of diffusion when the guiding wave field extends over the disordered topography. We rationalize mechanistically the emergent statistics by virtue of the wave-mediated resonant coupling between the droplet and topography, which produces an attractive wave potential about the localization region. This hydrodynamic analog, which demonstrates how a classical particle may localize like a wave, suggests new directions for future research in various areas, including active matter, wave localization, many-body localization, and topological matter.
Abel J. Abraham, Stepan Malkov, Frane A. Ljubetic, Matthew Durey, and Pedro J. Sáenz. Phys. Rev. X 14, 031047 – Published 17 September 2024
DOI:10.1103/PhysRevX.14.031047
