Phase Coexistence in Nonreciprocal Quorum-Sensing Active Matter

Motility and nonreciprocity are two primary mechanisms for self-organization in active matter. In a recent study [Phys. Rev. Lett. 131, 148301 (2023)], we explored their joint influence in a minimal model of two-species quorum-sensing active particles interacting via mutual motility regulation. Our results notably revealed a highly dynamic phase of chaotic chasing bands that is absent when either nonreciprocity or self-propulsion is missing. Here, we examine further the phase behavior of nonreciprocal quorum-sensing active particles, distinguishing between the regimes of weak and strong nonreciprocity. In the weakly nonreciprocal regime, this system exhibits multi-component motility-induced phase separation. We establish an analytical criterion for the associated phase coexistence, enabling a quantitative prediction of the phase diagram. For strong nonreciprocity, where the dynamics is chase-and-run-like, we numerically determine the phase behavior and show that it strongly depends on the scale of observation. In small systems, our numerical simulations reveal a phenomenology consistent with phenomenological models, comprising traveling phase-separated domains and spiral-like defect patterns. However, we show that these structures are generically unstable in large systems, where they are superseded by bulk phase coexistence between domains that are either homogeneous or populated by mesoscopic chasing bands. Crucially, this implies that collective motion totally vanishes at large scales, while the breakdown of our analytical criterion for this phase coexistence with multi-scale structures prevents us from predicting the corresponding phase diagram.