Single-File Diffusion of Active Brownian Particles

Abstract: Single-file diffusion (SFD) is a key mechanism underlying transport phenomena in confined physical and biological systems. In a typical SFD process, microscopic particles are restricted to moving in a narrow channel where they cannot pass one another, resulting in constrained motion and anomalous long-time diffusion. In this study, we use Brownian dynamics simulations and analytical theory to investigate the SFD of athermal active Brownian particles (ABPs), a minimal model of active colloids. Building on prior work (Phys. Rev. E 108, 064601 (2023)), where the kinetic temperature, pressure, and compressibility of the single-file ABP system were derived, we develop an accurate analytical expression for the mean square displacement (MSD) of a tagged particle. We find that the MSD exhibits ballistic behavior at short times, governed by the reduced kinetic temperature of the system. At long times, the characteristic subdiffusive scaling of SFD, $\langle (\Delta x)^2 \rangle \sim t^{1/2}$, is preserved. However, self-propulsion introduces significant changes to the 1D mobility, which we directly relate to the system's compressibility. Furthermore, we demonstrate that the generalized 1D mobility, originally proposed by Kollmann for equilibrium systems (Phys. Rev. Lett. 90, 180602 (2003)), can be extended to active systems with minimal modification. These findings provide a framework for understanding particle transport in active systems and for tuning transport properties at the microscale, particularly in geometries where motion is highly restricted.