Resonant diffusion of a gravitactic circle swimmer

TL;DR

This paper studies how a chiral active particle's long-time diffusion is resonantly enhanced by external torque near intrinsic angular drift, combining simulations and analytical models.

Contribution

It provides a detailed analysis of resonant diffusion in gravitactic circle swimmers, including analytic expressions and a harmonic oscillator model for the phenomenon.

Findings

Diffusivity sharply increases near the torque-induced resonance.

Analytic solutions relate diffusivity to eigenvalues of the noisy-driven pendulum.

Resonance is explained by bifurcation and eigenvalue vanishing.

Abstract

We investigate the dynamics of a single chiral active particle subject to an external torque due to the presence of a gravitational field. Our computer simulations reveal an arbitrarily strong increase of the long-time diffusivity of the gravitactic agent when the external torque approaches the intrinsic angular drift. We provide analytic expressions for the mean-square displacement in terms of eigenfunctions and eigenvalues of the noisy-driven-pendulum problem. The pronounced maximum in the diffusivity is then rationalized by the vanishing of the lowest eigenvalues of the Fokker-Planck equation for the angular motion as the rotational diffusion decreases and the underlying classical bifurcation is approached. A simple harmonic-oscillator picture for the barrier-dominated motion provides a quantitative description for the onset of the resonance while its range of validity is determined by the crossover to a critical-fluctuation-dominated regime.