Geometry-rectified transport of chiral active particles in a radial ratchet

Abstract

Structured environments organize active-particle currents by coupling propulsion and orientational dynamics to geometry. Translationally periodic ratchets can produce a rotation-frequency-dependent drift across equivalent unit cells, but the locked position remains spatially degenerate. In this paper, we show that a radially periodic landscape removes this degeneracy through self-referential feedback that weakens with orbital radius. Trajectories initialized within finite capture basins converge to preferred phase-locked radii, and the resulting locked orbits exhibit a chirality-odd transverse mobility under a weak radial force. Depinned trajectories instead organize into near-integer winding branches whose normalized mean drift approaches the associated branch label. The second harmonic of the radial potential reshapes the radial barriers and changes which branches are reached from a prescribed initial state. Near a locking boundary, an effective angular potential describes noise-activated phase slips and their first-passage statistics. The full radial dynamics shows how repeated slips accumulate into radial spreading. With short-range repulsion, the radial-well structure remains visible as the particles redistribute outward. Together, these results establish a geometric route for organizing frequency-dependent transport in patterned, substrate-confined active matter and may guide the design of chiral microrobotic and granular-roller systems.