Exploring diffraction with a pilot-wave model

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 microscopic 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, Y. {\&} Fort, E. Phys. Rev. Lett. 97, 154101, 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, A. et al. Phys. Rev. E 92, 013006, 2015; Pucci, G. et al. J. Fluid Mech. 835, 1136-1156, 2018; Rode, M. et al. Phys. Rev. Fluids 4, 104801, 2019). Here we use the pilot-wave model developed by Oza et al. (J. Fluid Mech. 737, 552-570, 2013) to explore the diffraction of a two-dimensional, wave-piloted particle by one-dimensional barriers. While our results are generally different from the Fraunhofer diffraction patterns in optics, the statistical distribution of deflection angles generally exhibits~multiple peaks, the number of which depends on the obstacle geometry.