The Three-Body Problem: Non-reciprocity and multibody interaction in acoustically levitated granular systems

When particles interact via a surrounding fluid medium, the coarse-grained interactions often break reciprocity. While recent advancements predominantly concentrate on effectively pairwise additive non-reciprocal interactions, non-reciprocity in fluid-mediated interactions inherently possesses a multibody character that cannot be linearly decomposed. Here, we highlight the inherent multibody and non-reciprocal nature of acoustic interactions, even in systems comprising as few as three particles. As in the classic gravitational three-body problem, a third particle greatly complicates the dynamics of the system; however, here it also renders non-reciprocal and non-pairwise effects dominant. In particular, we demonstrate that the interaction between two particles depends sensitively on the relative position of the third particle. We further show that this three-particle system harnesses energy from its non-reciprocal interaction, exhibiting emergent behavior such as self-propulsion and limit cycle. This minimal three-particle system not only explains how multibody, non-reciprocal interactions can lead to self-excitation in acoustic levitated systems but also offers a potential model for similar phenomena in other fluid-mediated interactions.