Wave-Like Statistics from Classical Active Particles with Internal Degrees Of Freedom

Wave-like spatial statistics in walking-droplet quantum analogs are typically attributed to spatial or temporal nonlocal wave effects. We show instead that such behavior arises generically from the low-dimensional nonlinear dynamics of an inertial active particle with internal degrees of freedom. Steady propulsion corresponds to internal fixed points whose spiral or chaotic relaxation organizes oscillatory ensemble densities. Local perturbations then produce Friedel-like patterns in open geometries and wave-like structure in confined geometries, extending hydrodynamic quantum analogs to inertial active matter more broadly.