# Statistical projection effects in a hydrodynamic pilot-wave system

Posted by sam on Jun 19, 2018 in Bibliography, Core Bibliography | 1 comment

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

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#### Recent Comments

- sam on A low‑cost, precise piezoelectric droplet‑on‑demand generator
- jitendra on A low‑cost, precise piezoelectric droplet‑on‑demand generator
- jitendra on A low‑cost, precise piezoelectric droplet‑on‑demand generator
- yeptube on Statistical projection effects in a hydrodynamic pilot-wave system
- sam on “Tunnel effect “
- Carlos on “Tunnel effect “
- yonglip on Particle in a box – DotWave Self-Interference tracking and statistics
- guest on bouncing droplets
- sam on EmQm17
- Paul Bancroft on EmQm17

#### Recent Posts

- Spin Lattice of walking droplets
- Statistical projection effects in a hydrodynamic pilot-wave system
- Quantum physics Dropwise
- EmQm17
- Walking droplet above cavities
- Faraday wave droplet dynamics : discret time analysis
- Tunneling with a hydrodynamic pilot-wave model
- Walking droplets in linear channels
- Self-propulsion and crossing statistics under random initial conditions
- A trajectory equation for walking droplets : hydrodynamic pilot-wave theory
- Influence of memory on trajectory in a harmonic potential
- A model for Faraday pilot waves over variable topography
- Non-specular reflection of walking droplets
- Self-attraction into spinning eigenstates of a mobile wave source by its emission back-reaction
- Onset of chaos in orbital pilot-wave dynamics

#### Stay informed !

#### Other Research teams

- Austrian Institute for Nonlinear Studies (AINS) – Gerhard Groessing
- Berkeley University – TAF LAB
- Caltech Mc Keon Research Group
- Instituto Nacional de Matemática Pura e Aplicada – Andre Nachbin and Carlos Galeano
- MIT – John BUSH
- St. Petersburg Nuclear Physics Institute – Dr. Valeriy Sbitnev
- Università degli Studi di Palermo – Pr. Diego Molteni –
- Université de Liège – Quandrops
- Université Paris Diderot – Yves Couder
- University of Bath – PAUL MILEWSKI
- University of Cambridge – Computer Laboratory – Dr Robert Brady

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