Analytical Theory of Chiral Active Particle Transport in a Fluctuating Density Field

TL;DR

This paper develops an analytical theory for chiral active particle transport in fluctuating density fields, revealing how chirality and density interactions influence diffusion, memory effects, and optimal transport conditions.

Contribution

The paper introduces a closed-form analytical framework for understanding chiral active Brownian particles in fluctuating environments, incorporating density coupling and temporal memory effects.

Findings

High initial diffusivity in dense regions due to transient drift

Existence of a crossover time for density homogenization

Non-monotonic dependence of steady-state diffusivity on chirality

Abstract

We develop a closed-form analytical theory for the transport of a chiral active Brownian particle (cABP) in three dimensions, moving through a fluctuating local density field that coarse-grains steric and dynamical interactions in a dense active medium. The density field is modeled as an Ornstein--Uhlenbeck process with finite correlation time $\tau$ and fluctuation strength $\sigma_\rho^2$, capturing both spatial variations and temporal memory. Within this framework, we derive exact expressions for the mean-squared displacement (MSD) and time-dependent diffusivity, showing how chirality and density coupling renormalize orientational persistence and generate dynamical crossovers. The theory predicts: (i) anomalously high initial diffusivity in denser regions, arising from a transient drift driven by local swim-pressure gradients; (ii) a finite crossover time $t_c$ for homogenizing density inhomogeneities, with steady-state diffusivity retaining memory of the initial environment; (iii) a non-monotonic $t_c(\Omega)$ with a global minimum at intermediate chirality, and a three-regime suppression of $D_\infty(\Omega)$ consistent with clustered phases in simulations; and (iv) a resonance-like peak in early-time oscillatory transport at an optimal chirality $\Omega^*$. The framework reproduces known scaling of $D_\infty$ with activity and chirality, while uncovering new memory effects and chirality-controlled optimal transport, offering predictive insight for biological circle swimmers and active metamaterials.