Mechanism for in-line speed oscillations in pilot-wave hydrodynamics

Walking droplets, which self-propel through a resonant interaction with their own wave field, offer a macroscopic realization of wave-particle duality previously thought exclusive to quantum particles. Recent work has elucidated the mechanism responsible for their orbital quantization in a rotating frame, highlighting the crucial role of non-local forces that arise from constructive interference of waves excited at stationary points on the walker's past trajectory. We here expand on this theory by investigating the emergence of an additional non-local force responsible for in-line speed oscillations, which play a pivotal role in the hydrodynamic analog of Friedel oscillations. Our analysis demonstrates that in-line speed oscillations result from interference disruptions caused by rapid changes in the walker's speed. By developing an extended minimal quantization model, we illustrate the various ways in which wave-mediated interactions may lead to the non-local forces responsible for hydrodynamic quantum analogs.