A hydrodynamic analog of the Aharanov-Bohm effect

A millimetric droplet may self-propel on the surface of a vibrating bath through a resonant interaction with its own wave field. The droplet and wave comprise a classical realization of wave-particle duality, a feature once thought to be unique to the quantum realm. The walking droplet (or `walker') system has been used to achieve hydrodynamic analogs of a number of canonical quantum effects. Here, we use it to develop and explore an analog to the Aharonov-Bohm (AB) effect, as has been a point of contention in the physics community since its discovery in 1959. The controversy surrounds the interpretation of vector potentials in quantum mechanics; specifically, are they fundamental physical objects or mathematical abstractions? In classical mechanics, only derivatives of potentials(specifically, fields) influence observable physics while, in quantum mechanics, the AB effect predicts interference effects even when all fields are zero. In our experiments, a walker is confined to an annular channel, inside which a submerged rotating disk creates a localized region of vorticity. Although the droplet does not interact directly with the vortex, its wave-field does. We examine how both the wave field and drop motion are altered by the vortex, and connect the observed behavior to the AB effect.