The active chiral random walk

We introduce a minimal and intuitive lattice model for an active chiral particle which exhibits persistence, reversal, and chirality in its dynamics. It is fully defined by a small set of microscopic parameters that provide transparent control over the resulting dynamics. By coarse-graining, we extract continuum equations and closed-form expressions for the velocity autocorrelation, off-diagonal directional correlation, mean-squared displacement, and long-time diffusion and odd diffusion coefficients. The complex parameter λ=qₚ+iqc thereby encodes the microscopic information on persistence (qₚ) and chirality (qc) of the walker. In a weak-turning limit, microscopically realized by infrequent reorientation events, the continuum description can be mapped onto well-established models of active matter. Outside this limit the discrete model exhibits finite-step dynamics, such as anti-persistent motion, that are not captured by a smooth angular-diffusion description. The model therefore provides a compact, exactly solvable, and readily tunable framework in which a small number of transparent microscopic parameters control chiral active transport.