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

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 $τ$ and fluctuation strength $σ_ρ^2$, 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 $t_c(Ω)$ with a global minimum at intermediate chirality, and a three-regime suppression of $D_\infty(Ω)$ consistent with clustered phases in simulations; and (iv) a resonance-like peak in early-time oscillatory transport at an optimal chirality $Ω^*$. 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.