Anomalous interference drives oscillatory dynamics in wave-dressed active particles

Abstract: A recent surge of discoveries has sparked significant interest in active systems where a particle moves autonomously in resonance with its self-generated wave field, leading to notable wave-mediated effects including new propulsion mechanisms, spontaneous oscillatory dynamics, and quantum-like phenomena. Drawing from an archetypical model of wave-dressed active particles, we unveil a wave-mediated non-local force driving their dynamics, arising from the particle's path memory and an unconventional form of wave interference near jerking points, locations where the particle's velocity changes rapidly. In contrast to the typical case of constructive interference at points of stationary phase, waves excited by the particle near jerking points avoid cancellation through rapid changes in frequency. Through an asymptotic analysis, we derive the wave force from jerking points, revealing it as an elusive but crucial remnant of the particle's past motion that underlies a range of phenomena previously regarded as disparate -- including in-line speed oscillations, wave-like statistics in potential wells, and non-specular reflections -- and places them within a unified mechanistic framework resulting from generic wave superposition principles.