Zoology of collective patterns modulated by non-reciprocal, long-range interactions

We investigate active particles that exhibit long-range interactions only restricted by a field of view, which is characterized by an angle $\beta$. We show that constraining attractive interactions to a field of view leads to the emergence of a complex pattern that exhibits - depending on the value of $\beta$ and initial conditions - significantly different topologies and transport properties. We find, in two dimensions, a nematic closed filament in the form of a ring that moves as a chiral active particle, a closed polar filament with one singular topological point that exhibits net polar order and moves ballistically, a structure with two singular topological points that rotates, or an open polar filament that behaves as a persistent random walk. Furthermore, we investigate the process that transforms one structure into another by slowly varying $\beta$ and observe that the process is non-reversible and presents strong hysteresis. Finally, we find that in three dimensions similar patterns also emerge. The analysis sheds light on the physics of single-species active particles with long-range, non-reciprocal interactions in two and three dimensions, characterized by the absence of gas phases, and provides evidence that in these systems, topological and transport properties are closely related.