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

Abstract

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.

arXiv comment8 pages, 6 figures

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