Diffusion of active chiral particles

TL;DR

This paper analytically and numerically investigates the diffusion behavior of chiral active Brownian particles in three dimensions, revealing oscillatory kurtosis dynamics and evidence of anomalous yet Brownian diffusion.

Contribution

It introduces an analytical framework for the probability density of chiral active particles, including explicit calculations of diffusion and shape dynamics, and uncovers novel oscillatory and anomalous diffusion phenomena.

Findings

Oscillations in kurtosis between Gaussian and shell-shaped distributions

Explicit time dependence of mean squared displacement and distribution shape

Evidence of anomalous, yet Brownian, diffusion in particle ensembles

Abstract

The diffusion of chiral active Brownian particles in three-dimensional space is studied analytically, by consideration of the corresponding Fokker-Planck equation for the probability density of finding a particle at position $\boldsymbol{x}$ and moving along the direction $\hat{\boldsymbol{v}}$ at time $t$, and numerically, by the use of Langevin dynamics simulations. The analysis is focused on the marginal probability density of finding a particle at a given location and at a given time (independently of its direction of motion), which is found from an infinite hierarchy of differential-recurrence relations for the coefficients that appear in the multipole expansion of the probability distribution which contains the whole kinematic information. This approach allows the explicit calculation of the time dependence of the mean squared displacement and the time dependence of the kurtosis of the marginal probability distribution, quantities from which the effective diffusion coefficient and the "shape" of the positions distribution are examined. Oscillations between two characteristic values were found in the time evolution of the kurtosis, namely, between the value that corresponds to a Gaussian and the one that corresponds to a distribution of spherical shell shape. In the case of an ensemble of particles, each one rotating around an uniformly-distributed random axis, it is found evidence of the so called effect "anomalous, yet Brownian, diffusion", for which particles follow a non-Gaussian distribution for the positions yet the mean squared displacement is a linear function of time.