Universal winding laws in chiral active motion

Abstract

Chiral active particles, from bacteria and sperm cells to engineered microswimmers, undergo persistent motion that breaks both time-reversal and mirror symmetries. This broken mirror symmetry leaves geometric signatures in trajectories that cannot be captured by conventional measures like position fluctuations. Here we identify the signed area and winding angle as key observables to characterize the geometric and topological aspects of the trajectories of chiral active particles. Combining theory, experiment, and computer simulations, we demonstrate that these observables exhibit universal growth laws and fluctuation statistics that are independent of propulsion details. The presence of chirality generates multiple off-centred closed loops in the trajectories, resulting in a linear temporal growth of the signed area and a much slower logarithmic growth for the winding angle. Our work uncovers universal trajectory-level signatures of chirality and provides a unifying description of chiral dynamics in active matter.

arXiv commentNew version, including experiments