# Statistical projection effects in a hydrodynamic pilot-wave system

ABSTRACT :

“Millimetric liquid droplets can walk across the surface of a vibrating fluid bath, self-propelled through a resonant interaction with their own guiding or ‘pilot’ wave fields. These walking droplets, or ‘walkers’, exhibit several features previously thought to be peculiar to the microscopic, quantum realm. In particular, walkers confined to circular corrals manifest a wave-like statistical behaviour reminiscent of that of electrons in quantum corrals. Here we demonstrate that localized topological inhomogeneities in an elliptical corral may lead to resonant projection effects in the walker’s statistics similar to those reported in quantum corrals. Specifically, we show that a submerged circular well may drive the walker to excite specific eigenmodes in the bath that result in drastic changes in the particle’s statistical behaviour. The well tends to attract the walker, leading to a local peak in the walker’s position histogram. By placing the well at one of the foci, a mode with maxima near the foci is preferentially excited, leading to a projection effect in the walker’s position histogram towards the empty focus, an effect strongly reminiscent of the quantum mirage. Finally, we demonstrate that the mean pilot-wave field has the same form as the histogram describing the walker’s statistics.”

Sáenz, P. J., Cristea-Platon, T., & Bush, J. W. (2018). Statistical projection effects in a hydrodynamic pilot-wave system. *Nature Physics*, *14*(3), 315.

http://math.mit.edu/~bush/wordpress/wp-content/uploads/2017/12/Saenz-NatPhys-2017-.pdf

# Non-specular reflection of walking droplets

Abstract : Since their discovery by Yves Couder and Emmanuel Fort, droplets walking on a vibrating liquid bath have attracted considerable attention because they unexpectedly exhibit certain features reminiscent of quantum particles. While the behaviour of walking droplets in unbounded geometries has to a large extent been rationalized theoretically, no such rationale exists for their behaviour in the presence of boundaries, as arises in a number of key quantum analogue systems. We here present the results of a combined experimental and theoretical study of the interaction of walking droplets with a submerged planar barrier. Droplets exhibit non-specular reflection, with a small range of reflection angles that is only weakly dependent on the system parameters, including the angle of incidence. The observed behaviour is captured by simulations based on a theoretical model that treats the boundaries as regions of reduced wave speed, and rationalized in terms of momentum considerations.

Pucci, G., Sáenz, P. J., Faria, L. M., & Bush, J. W. (2016). Non-specular reflection of walking droplets. *J Fluid Mech*, *804*, R3.

http://math.mit.edu/~bush/wordpress/wp-content/uploads/2016/09/Pucci-JFM-2016.pdf