# The pilot-wave dynamics of walking droplets

@article{Harris2013ThePD, title={The pilot-wave dynamics of walking droplets}, author={Daniel M. Harris and John W. M. Bush}, journal={Physics of Fluids}, year={2013}, volume={25}, pages={091112} }

Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters.

## 19 Citations

### Simulations of pilot-wave dynamics in a simple harmonic potential

- Physics
- 2017

We present the results of a numerical investigation of droplets walking in a harmonic potential. Particular attention is given to delineating the parameter regimes in which periodic and chaotic…

### Scattering theory of walking droplets in the presence of obstacles

- Physics
- 2016

We aim to describe a droplet bouncing on a vibrating bath using a simple and highly versatile model inspired from quantum mechanics. Close to the Faraday instability, a long-lived surface wave is…

### Faraday pilot-wave dynamics: modelling and computation

- PhysicsJournal of Fluid Mechanics
- 2015

A millimetric droplet bouncing on the surface of a vibrating fluid bath can self-propel by virtue of a resonant interaction with its own wave field. This system represents the first known example of…

### Faraday Pilot-Wave Hydrodynamics: Modelling and Computation

- Physics
- 2016

A millimetric droplet bouncing on the surface of a vibrating ﬂuid bath can self-propel by virtue of a resonant interaction with its own wave ﬁeld (Couder et al. 2005a; Proti`ere et al. 2006). This…

### Oscillons, walking droplets, and skipping stones (an overview)

- Physics
- 2021

This article considers additional phenomena that complement the earlier topics addressed by Ibrahim [(Liquid Sloshing Dynamics: Theory and Applications. Cambridge University Press, Cambridge, 2005),…

### Shedding light on pilot-wave phenomena

- Physics
- 2016

FIG. 1. (a) A droplet of an approximate diameter of 1 mm bounces on the surface of a vibrating oil bath. (b) For sufficiently large values of the vertical forcing, a droplet may spontaneously…

### Pilot-Wave Hydrodynamics

- Physics
- 2015

Yves Couder, Emmanuel Fort, and coworkers recently discovered that a millimetric droplet sustained on the surface of a vibrating fluid bath may self-propel through a resonant interaction with its own…

### Kuramoto-Like Synchronization Mediated through Faraday Surface Waves

- PhysicsFluids
- 2020

A new class of problems in free surface hydrodynamics appeared after the groundbreaking discovery by Yves Couder and Emmanuel Fort. A bouncing droplet in association with Faraday surface waves gives…

### Hydrodynamic quantum analogs

- PhysicsReports on progress in physics. Physical Society
- 2020

The walking droplet system discovered by Yves Couder and Emmanuel Fort presents an example of a vibrating particle self-propelling through a resonant interaction with its own wave field, and a generalized theoretical framework that provides a mathematical bridge between the hydrodynamic pilot-wave system and various realist models of quantum dynamics is described.

## References

SHOWING 1-10 OF 13 REFERENCES

### Wavelike statistics from pilot-wave dynamics in a circular corral.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2013

It is demonstrated 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.

### Drops walking on a vibrating bath: towards a hydrodynamic pilot-wave theory

- PhysicsJournal of Fluid Mechanics
- 2013

Abstract We present the results of a combined experimental and theoretical investigation of droplets walking on a vertically vibrating fluid bath. Several walking states are reported, including pure…

### Single-particle diffraction and interference at a macroscopic scale.

- PhysicsPhysical review letters
- 2006

A droplet bouncing on a vertically vibrated bath can become coupled to the surface wave it generates and become a "walker" moving at constant velocity on the interface, and diffraction or interference patterns are recovered in the histogram of the deviations of many successive walkers.

### Unpredictable tunneling of a classical wave-particle association.

- PhysicsPhysical review letters
- 2009

This work investigates the motion of a walker when it collides with barriers of various thicknesses and shows that this wave-particle association has a nonlocality sufficient to generate a quantumlike tunneling at a macroscopic scale.

### Particle–wave association on a fluid interface

- PhysicsJournal of Fluid Mechanics
- 2006

A small liquid drop can be kept bouncing on the surface of a bath of the same fluid for an unlimited time when this substrate oscillates vertically. With fluids of low viscosity the repeated…

### Level splitting at macroscopic scale.

- PhysicsPhysical review letters
- 2012

This work shows that the bound states are driven by the wave interaction between the walkers and it observes a level splitting at macroscopic scale induced by the rotation, the classical equivalent to Zeeman splitting of atomic energy levels.

### Drops bouncing on a vibrating bath

- PhysicsJournal of Fluid Mechanics
- 2013

Abstract We present the results of a combined experimental and theoretical investigation of millimetric droplets bouncing on a vertically vibrating fluid bath. We first characterize the system…

### Path-memory induced quantization of classical orbits

- PhysicsProceedings of the National Academy of Sciences
- 2010

A droplet bouncing on a liquid bath can self-propel due to its interaction with the waves it generates. The resulting “walker” is a dynamical association where, at a macroscopic scale, a particle…

### From bouncing to floating: noncoalescence of drops on a fluid bath.

- PhysicsPhysical review letters
- 2005

An analysis using lubrication theory accounts for most of the observations, showing that a steady regime where a drop can be kept bouncing for any length of time is found.

### Confinement of Electrons to Quantum Corrals on a Metal Surface

- PhysicsScience
- 1993

Tuning spectroscopy performed inside of the corrals revealed a series of discrete resonances, providing evidence for size quantization and STM images show that the corral's interior local density of states is dominated by the eigenstate density expected for an electron trapped in a round two-dimensional box.