A case of wave-particle duality at macroscopic scale, quantum-like behaviours emerging out of memory driven trajectories

Laboratoire Matière et Systèmes Complexes
Université Paris Diderot -Paris7

It is usually assumed that the quantum wave-particle duality can have no counterpart in classical physics. Similarly, the probabilistic aspects of quantum dynamics are often said to be intrinsic and to have no possible relation with underlying unresolved dynamical phenomena.
We revisited these questions when we investigated the properties of a droplet bouncing on a vibrated bath. In this system, a propagative wave-particle association appears when the droplet couples to the surface wave it excites. Through several experiments on this non-quantum system we addressed a general question. How can a continuous and spatially extended wave have a common dynamics with a localized and discrete droplet? Surprisingly quantum-like behaviors emerge from these experiments. Both a form of uncertainty and a form of quantization are observed. The relation of this system with the pilot wave models of quantum mechanics will be discussed. Our experiment turns out to implement a situation close to the de Broglie hypothesis of a "double solution" where an individual wave guides the particle in the physical space, and a Schrödinger-type wave accounts for its statistical behaviour. In our system the guiding wave has a specific asset: its interference structure contains what we called a "path memory" of the drop recent trajectory. Our results suggest that this temporal non-locality of the pilot wave is essential in generating the observed quantum-like effects.