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

Abstract

We develop a closed-form analytical theory for the transport of a chiral active Brownian particle in three dimensions, moving through a fluctuating local density field that models steric and dynamical interactions in a dense active medium. The density field is modeled as an Ornstein--Uhlenbeck process with finite correlation time $\ddot{I}„$ and fluctuation strength $\ddot{I}{ƒ}_{\ddot{I}}{}^2$, capturing both spatial fluctuations and temporal memory. Within this framework, we derive exact expressions for the mean-squared displacement and time-dependent diffusivity, revealing how chirality and density coupling jointly renormalise orientational persistence and generate nontrivial dynamical crossovers. The theory predicts: (i) anomalously high initial diffusivity for particles starting in locally denser regions, arising from a transient active drift driven by local swim-pressure gradients; (ii) a finite crossover time $t_c$ for homogenising density inhomogeneities, with a transient dependence of the dynamics on the initial local density environment which arises from the non-equilibrium evolution of density fluctuations and does not persist when averaging over stationary initial conditions ($\ddot{I}{}_0=\ddot{I}{}_{\infty }$) ; (iii) a non-monotonic $t_c(\hat{I}\text{c◯})$ with a global minimum at intermediate chirality, and a three-regime suppression of long-time diffusivity $D_{\infty }(\hat{I}\text{c◯})$, consistent with micro-clustered phases observed in simulations; and (iv) a resonance-like peak in the early-time oscillatory strength of the mean-squared displacement at an optimal chirality $\hat{I}{\text{c◯}}^{\ast }$, set by the interplay of orientational diffusion, density-field decorrelation, and imposed rotation. The framework captures the qualitative dependence of $D_{\infty }$ on $Pe$ and $\hat{I}\text{c◯}$, {where Pe denotes the Péclet number}, while uncovering chirality-dependent transport features in active matter.