Spatiotemporal Characterization of Active Brownian Dynamics in Channels

TL;DR

This paper analytically investigates the behavior of active Brownian particles in confined channels, revealing how activity influences boundary accumulation and first-passage times across different regimes.

Contribution

It provides the first analytical predictions for first-passage properties and spatial distributions of confined active Brownian particles, utilizing a novel duality approach.

Findings

Active motion reduces mean first-passage time compared to passive diffusion.

The stationary distribution near walls is characterized by boundary accumulation.

Siegmund duality links propagators with different boundary conditions.

Abstract

Accumulation at boundaries represents a widely observed phenomenon in active systems with implications for microbial ecology and engineering applications. To rationalize the underlying physics, we provide analytical predictions for the first-passage properties and spatial distributions of a confined active Brownian particle (ABP). We show that ABPs with absorbing and hard-wall boundary conditions are Siegmund duals, yielding a direct mapping between the propagators of the two problems. We analyze the system across low and high activity regimes -- quantifying persistent motion relative to diffusion -- and show that active motion, together with a favorable initial orientation, typically lowers the mean first-passage time relative to passive diffusion. Notably, the full time-dependent propagator between hard walls approaches a wall-accumulated stationary state given by the derivative of the splitting probability as a consequence of Siegmund duality.