Walking droplets over submerged variable topography

Variable bottom topography has emerged as a powerful element to develop a new range of hydrodynamic quantum analogs with walking droplets, including analogs of the quantum mirage, Friedel oscillations, and most recently, Anderson localization. These walking droplets, or "walkers", self-propel across the surface of a vibrating fluid bath through a resonant interaction with their own wave fields. When the bath depth is comparable to the wavelength of the guiding waves, the walker's motion is influenced by the features of the submerged topography. Here, we describe the role of variable bottom topography as an analog of the quantum potential. We focus on Anderson localization – a remarkable phenomenon where quantum particles come to rest in a disordered medium despite their energy exceeding the background potential. We find similar localization in our hydrodynamic analog system when the wave field extends over a random topography. Moreover, we explore the parameter regime to develop a new analog of weak localization, wherein disorder induces diffusive particles to exhibit an enhanced return to the origin. Our experimental findings are rationalized through the emergence of an effective wave potential.