Harris, D. M., Moukhtar, J., Fort, E., Couder, Y., & Bush, J. W. (2013). Wavelike statistics from pilot-wave dynamics in a circular corral. *Physical Review E*, *88*(1), 011001.

*Abstract : Bouncing droplets can self-propel laterally along the surface of a vibrated fluid bath by virtue of a resonant interaction with their own wave field. The resulting walking droplets exhibit features reminiscent of microscopic quantum particles. Here we present the results of an experimental investigation of droplets walking in a circular corral. We demonstrate that a coherent wavelike statistical behavior emerges from the complex underlying dynamics and that the probability distribution is prescribed by the Faraday wave mode of the corral. The statistical behavior of the walking droplets is demonstrated to be analogous to that of electrons in quantum corrals.*

http://math.mit.edu/~bush/wordpress/wp-content/uploads/2013/07/Harris-Corrals-2013.pdf

Statistical behavior of a walking droplet in a confined geometry

I am very glad you exist, as it was hard for me to corral all the papers (no pun intended). This particular one is very interesting as it establishes a parallel between the Schrodinger wave and the Faraday wave, my main question is around the 2D vs 3D. Couder talks about that limitation of the model, that real ‘quantum systems’ would exist in 3D but this says the exact parallel in electron systems would be 2D.

Brady has a 3D analog to walking droplet

http://www.cl.cam.ac.uk/~rmb4/sonons/sonons.html