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 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 τ and fluctuation strength σ_{ρ}^{2}, capturing both spatial fluctuations and temporal memory. Within this framework, we derive exact expressions for the mean-square displacement and time-dependent diffusivity, revealing how chirality and density coupling jointly renormalize 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 homogenizing density inhomogeneities, with a transient dependence of the dynamics on the initial local density environment which arises from the nonequilibrium evolution of density fluctuations and does not persist when averaging over stationary initial conditions (ρ_{0}=ρ_{∞}); (iii) a nonmonotonic t_{c}(Ω) with a global minimum at intermediate chirality, and a three-regime suppression of long-time diffusivity D_{∞}(Ω), consistent with microclustered phases observed in simulations; and (iv) a resonance like peak in the early-time oscillatory strength of the mean-square displacement at an optimal chirality Ω^{*}, set by the interplay of orientational diffusion, density-field decorrelation, and imposed rotation. The framework captures the qualitative dependence of D_{∞} on Pe and Ω, where Pe denotes the Péclet number, while uncovering chirality-dependent transport features in active matter, offering a qualitative perspective for understanding transport in biological systems and suggesting possible directions for designing active materials.