Anomalous interference drives oscillatory dynamics in wave-dressed active particles

A recent surge of discoveries has sparked significant interest in driven-dissipative systems where a particle self-propels due to a resonant interaction with its self-generated wave field. These wave-dressed active particles frequently undergo rapid changes in velocity due to a variety of factors, including boundaries altering their direction of motion, media inhomogeneities distorting their wave field, and direct interactions with their own wave field. We deduce the emergence of a nonlocal wave-mediated force caused by an anomalous type of wave interference in the vicinity of jerking points, places where the particle's velocity changes most rapidly. In contrast to the typical case of constructive interference at points of stationary phase, waves excited by the particle at jerking points avoid cancellation through rapid changes in frequency. Through an asymptotic analysis, we approximate the wave force at jerking points, allowing us to rationalize in-line speed oscillations, non-specular reflections off potential walls, and wave-like statistics in certain potential wells. The results we derive are generic, and thus applicable to a relatively large class of wave-dressed active particles.