Synchronization and exceptional points in nonreciprocal active polar mixtures

Abstract: Many biological and synthetic active matter systems consist of different particle types that interact via nonreciprocal couplings. A striking consequence of such interactions is the spontaneous emergence of time-dependent states that break parity-time symmetry. On the field-theoretical level, the transition to these states is marked by so-called exceptional points. However, their precise impact on observable particle dynamics remains poorly understood. In this study, we address this gap by providing a scale-bridging view of a minimal active mixture with nonreciprocal polar interactions. We find that nonreciprocity induces chiral motion on the particle level, yet no full, homogeneous synchronization. Instead, we observe various behaviors, ranging from fully synchronized clusters to chimera-like states. The nonreciprocity-induced spontaneous chirality increases with the degree of nonreciprocity and peaks at coupling strengths associated with exceptional points.