HQA of Friedel oscillations

When a walking droplet approaches a submerged well, it is drawn in along an Archimedean spiral. In exiting the well, the drop executes in-line speed oscillations that result in a coherent statistical signature analogous to Friedel oscillations.

We present a macroscopic analog of an open quantum system, achieved with a classical pilot-wave system. Friedel oscillations are the angstrom-scale statistical of an impurity on a metal surface, concentric circular modulations in the probability density function of the surrounding electron sea. We consider a millimetric drop, propelled by its own wave field along the surface of a vibrating liquid bath, interacting with a submerged circular well. An ensemble of drop trajectories displays a statistical signature in the vicinity of the well that is strikingly similar to Friedel oscillations. The droplet trajectories reveal the dynamical roots of the emergent statistics. Our study elucidates a new mechanism for emergent quantum-like statistics in pilot-wave hydrodynamics and so suggests new directions for the nascent field of hydrodynamic quantum analogs.

See paper: Sáenz, P.J., Cristea-Platon, T. and Bush, J.W.M. Bush (2020)