Comparison between the walking droplet and the electron behaviour inside a chaotic stadium cavity

The walking droplet experiment has received particular attention in the last fifteen years because it represents the first known example of a macroscopic pilot-wave system that exhibits behaviours thought to be exclusive to the microscopic quantum realm. Most efforts about walking droplets have focused on the experimental analysis in a "fluid mechanics" framework and on its mathematical modeling. On the other hand, the stadium billiard, one of the first 2D concave chaotic geometries introduced by Bunimovich, has been actively studied for these last decades because of the drastic differences observed between classical and quantum particles behaviour in such geometry. Consequently, the objective of this master thesis is to analyze the behaviour of walking droplets inside the Bunimovich stadium billiard and compare it with the behaviours of classical and quantum particles in similar conditions. To fulfil this objective, a complete low-cost experimental setup has been developed for the observations of walking droplets, comprising : a fabricated bath stuck on the membrane of a loudspeaker for the vertical shaking, a 3-axis accelerometer providing real-time measurements on PC, a droplet generator based on a piezoelectric buzzer and a fixed camera recording top view images of the droplet motion which are post-processed with Matlab. The imperfect horizontality of the developed setup is shown to lead to an effective Faraday instability threshold lower than the scientific consensus for the same forcing parameters (Γ_F,e = 2.3[g] < Γ_F = 4.144[g]). As it prevents us to correctly estimate the memory parameter Me, the conducted experiments are instead described in terms of shaking amplitude Γ and estimated tilt angles of the bath θ and β. It is observed that the walking droplet long-term evolution in a stadium billiard presents a clear scarring pattern, informing on the existence of preferred "probable positions" of the droplet inside the billiard. The scarring pattern, while very similar to a typical shape found in quantum simulations, is surprisingly much more robust against forcing variations than the scars observed for electrons.