This is the website of a team of researchers based in Paris who study various aspects of the wave-particle duality exhibited by droplets bouncing on a vibrated liquid substrate. It presents an outlook on their work together with a collection of films they recorded.

The actors of this collective enterprise have been :
Vincent Bacot, Christian Borghesi, Arezki Boudaoud, Yves Couder, Aurelien Decelle, Antonin Eddi, Emmanuel Fort, Charles-Henri Gautier, Maxime Hubert, Matthieu Labousse, Marc Miskin, Frédéric Moisy, Julien Moukhtar, Stéphane Perrard, Suzie Protière, Alain Roger, Maurice Rossi, Eric Sultan, Denis Terwagne.


Masses and waves have long been the constitutive elements of classical physics. The wave-particle duality, which characterizes the behaviour of elementary physical objects on a microscopic scale, appeared only with quantum mechanics. Until now, this duality had no equivalent at the macroscopic scale, where masses and waves remained objects of a different nature.
Approximately ten years ago we were brought to reconsider this latter question while investigating the behaviour of bouncing droplets. Our experiments revealed that in this system there existed regimes in which the bouncing droplet coupled to the wave to form a symbiotic propagative structure. We were thus led to ask ourselves if any of its dynamical properties could be compared to those characterizing the quantum wave-particle duality. It turned out that such a comparison was often possible. This was by itself a big surprise. Walkers have a macroscopic scale and have no relation to the Planck constant. They are not Hamiltonian, they are dissipative structures sustained by an external forcing. Furthermore, their associated waves are not probability waves but physical waves propagating on a material substrate. Precisely because of this distance, the results obtained with walkers suggest that some phenomena could be general enough to overcome the classical-quantum barrier and be common to the two worlds. If this can be proven true, experiments performed at classical scale could shed light on non-observable phenomena underlying quantum effects.
The present web site is aimed at giving a brief summary of our approach, illustrated by films recorded during the development of this research. For each of these experiments the reader can find a more complete discussion in various articles we wrote, their pdfs can be accessed directly. References are also given to results obtained on the same subject by other teams.


In the following we will first show how droplets bounce on a vibrated liquid substrate (see I). In so doing they generate surface waves by which they can interact at a distance forming various2D crystalline structures (see II). We will then show how the droplet can couple to its own wave to become the core of a self-propelled "dual walker" (see III). A specific asset of these walkers is that their associated waves are standing Faraday waves. These waves decay slowly, being almost sustained by the imposed oscillation. For this reason the structure of the global wave field generated by the drop contains a recorded memory of its past motion (see IV). When the drop is constrained into orbiting motions (see V), the memory effect generates global wave fields and the possible trajectories become characterized by their quantization . Finally several experiments devoted to orbiting, diffraction, tunnel effect, or the confinement in corrals, have revealed that chaotic regimes can be generated that are responsible for the emergence of statistical properties (see VI).