Chirality, confinement, and dimensionality govern re-entrant transitions in active matter

Abstract

The non-equilibrium dynamics of individual chiral active particles underpin the complex behavior of chiral active matter. Here, we present an exact analytical framework, supported by simulations, to characterize the steady states of two-dimensional chiral active Brownian particles and three-dimensional torque-driven counterparts in a harmonic trap. Using a Laplace-transform approach to the Fokker–Planck equation, we derive closed-form expressions for displacement moments and excess kurtosis, providing a precise probe of non-Gaussian statistics. Our analysis reveals three distinct regimes characterized by bimodal distributions with off-center peaks, Gaussian-like distributions, and weakly heavy-tailed distributions unique to two dimensions. We show that dimensionality plays a decisive role: in two dimensions, increasing chirality suppresses activity and restores Gaussian-like behavior, whereas in three dimensions, torque sustains anisotropic steady states and preserves non-Gaussianity even at high chirality. These behaviors are captured by simple active length-scale arguments that map the boundaries between Gaussian-like and non-Gaussian states. Our results offer concrete experimental signatures—including kurtosis crossovers, off-center peaks, and torque-induced anisotropy—that establish confinement as a powerful tool to probe and control chiral and torque-driven active matter.