Discrete dynamical model for the hydrodynamic analog of a quantum mirage

Abstract

Recently discrete dynamical models of walking droplet dynamics have allowed for fast numerical simulations of their horizontal chaotic motion and consequently the long-time statistical distribution of the droplet position. We develop a discrete model for walkers on an elliptical corral with two dominant eigenmodes. These eigenmodes are excited periodically with each having random, but correlated, weights. At each iteration the model computes the horizontal propulsion of the droplet due to impacts with the fluid bath. The propulsion is calculated based on the interaction of the droplet and the wavefield produced by the eigenmode excitations, with the droplet being propelled perpendicular (rather than parallel) to the wave gradient. We record the long-time statistics, and remarkably for a dynamical system with some non-physical assumptions, they are qualitatively similar to that of experiments.