# Path-memory induced quantization of classical orbits

@article{Fort2010PathmemoryIQ, title={Path-memory induced quantization of classical orbits}, author={Emmanuel Fort and Antonin Eddi and Arezki Boudaoud and Julien Moukhtar and Yves Couder}, journal={Proceedings of the National Academy of Sciences}, year={2010}, volume={107}, pages={17515 - 17520} }

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 (the droplet) is driven by a pilot-wave field. A specificity of this system is that the wave field itself results from the superposition of the waves generated at the points of space recently visited by the particle. It thus contains a memory of the past trajectory of the particle. Here, we investigate…

## 174 Citations

Probabilities and trajectories in a classical wave-particle duality

- Physics
- 2012

Several recent experiments were devoted to walkers, structures that associate a droplet bouncing on a vibrated liquid with the surface waves it excites. They reveal that a form of wave-particle…

Self-organization into quantized eigenstates of a classical wave-driven particle.

- PhysicsNature communications
- 2014

This work investigates the behaviour of particles or singularities with physical waves when confined in a two-dimensional harmonic potential well and shows that these trajectories are intertwined with the dynamical build-up of central wave-field modes.

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.

Information stored in Faraday waves: the origin of a path memory

- PhysicsJournal of Fluid Mechanics
- 2011

On a vertically vibrating fluid interface, a droplet can remain bouncing indefinitely. When approaching the Faraday instability onset, the droplet couples to the wave it generates and starts…

Classical pilot-wave dynamics: The free particle.

- PhysicsChaos
- 2021

A number of new dynamical states in which the free particle executes self-induced wobbling and precessing orbital motion are reported, including the chaotic regime arising when the time scale of the wave decay is long relative to that of particle motion.

Dynamics, emergent statistics, and the mean-pilot-wave potential of walking droplets.

- PhysicsChaos
- 2018

A millimetric droplet may bounce and self-propel on the surface of a vertically vibrating bath, where its horizontal "walking" motion is induced by repeated impacts with its accompanying Faraday wave field, which reveals a number of dynamical regimes, including those characterized by stationary bouncing droplets trapped by the harmonic potential.

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…

Non-Hamiltonian features of a classical pilot-wave dynamics.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2014

It is demonstrated that the interaction with the recently emitted waves can be modeled by a Rayleigh-type friction, and a basic framework for further investigations of wave-particle interactions when memory effects are included.

Exploring orbital dynamics and trapping with a generalized pilot-wave framework.

- PhysicsChaos
- 2018

The effects of an imposed potential with both oscillatory and quadratic components on the dynamics of walking droplets are explored and the mean wavefield from a chaotic trajectory is computed and its predicted relationship with the particle's probability density function is confirmed.

Dynamics and statistics of wave-particle interactions in a confined geometry.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2014

This article presents a toy model of the coupling between a particle and a confined standing wave that shows that deterministic wave-particle coupling expressed in its simplest form can account for some quantumlike behaviors.

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