Single-particle Fraunhofer diffraction in a classical pilot-wave model

Abstract

Walking oil droplets offer a qualitative, classical analog of single-particle diffraction. Making this analog quantitative has proven challenging, leading recent authors to conjecture that no classical pilot-wave model could exhibit Fraunhofer diffraction. We revisit the problem with the recent, Lagrangian pilot-wave model of Darrow and Bush [Symmetry 16, 149 (2024)], and find agreement with both single- and double-slit Fraunhofer patterns. We identify two distinct dynamical features that enable our model to capture Fraunhofer diffraction and distinguish it from previous classical pilot-wave models.