Pilot-wave hydrodynamics in confined geometries

In pilot-wave hydrodynamics, a millimetric oil droplet in turn generates and is propelled by waves induced by its bouncing on a vertically vibrating liquid bath. This hydrodynamic system exhibits wave-particle duality on the macroscopic scale of a form envisaged by Louis de Broglie in his now century-old `double-solution' theory of quantum mechanics. When the droplet moves in a confined geometry (a corral), a rich set of statistical patterns emerge in the droplet's position histogram, some of which are reminiscent of those arising in the quantum corral. In the hydrodynamic corrals, the statistical behavior of the droplet can be rationalized in terms of an underlying dynamical theory. Three distinct mechanisms are detailed here, which represent the three central paradigms for emergent quantum behavior in pilot-wave hydrodynamics. In the first, droplet motion is marked by intermittent switching between unstable periodic orbits. In the second, droplet speed oscillations give rise to a coherent statistical signature. In the third, non-resonant effects between the droplet and its pilot-wave give rise to ponderomotive effects.