Active Brownian Dynamics in Channels: First-Passage and Spatiotemporal Properties via Siegmund Duality.

Authors

Yanis Baouche, Mathis Guéneau, Christina Kurzthaler

Published in

Physical review letters. Volume 137. Issue 13. Pages 138301. Sep 25, 2026.

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 study the first-passage properties and spatial distributions of an active Brownian particle (ABP) in a channel. Leveraging Siegmund duality, we establish a direct mapping between the propagators of ABPs with absorbing and hard-wall boundary conditions, yielding analytical results in both 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.

PMID:
42854152
Bibliographic data and abstract were imported from PubMed on 10 Oct 2026.

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