Diffraction of particles in a hydrodynamic pilot-wave theory

The seminal experiments of Yves Couder and Emmanuel Fort demonstrated that a droplet walking on the surface of a fluid bath may exhibit behavior thought to be peculiar to the quantum realm. One of their experiments suggested that single-particle diffraction and interference may be obtained when a walker crosses a single- or a double-aperture between submerged barriers (Couder & Fort Phys. Rev. Lett. 2006). Later experiments with finer control of experimental parameters yielded different results, thus reopening the question of the extent of the analogy between walkers and quantum particles (Andersen et al. Phys. Rev. E 2015; Pucci et al. J. Fluid Mech. 2018; Rode et al. Phys. Rev. Fluids 2019; Ellegaard & Levinsen, Phys. Rev. E 2020). Here we use the pilot-wave model developed by Oza et al. (J. Fluid Mech. 2013) to explore numerically the diffraction of a wave-driven particle by barriers, which are represented as an array of reflecting point sources of waves. The statistical distribution of the particle's deflected position generally exhibits multiple peaks, the number of which depends on the obstacle geometry and the bath's forcing acceleration. We will discuss the similarities and differences between these statistical distributions and the Fresnel and Fraunhofer diffraction patterns in optics.