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

Yanis Baouche1,*, Mathis Guéneau1,*, and Christina Kurzthaler1,2,3,†

  • *These authors contributed equally to this work.
  • †Contact author: ckurzthaler@pks.mpg.de
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Phys. Rev. Lett. 137, 138301 – Published 21 September, 2026

DOI: https://doi.org/10.1103/g83n-r4hs

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.

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Phys. Rev. Lett. 137, 138301– Published 21 September, 2026
  • Received 31 March 2026
  • Accepted 24 August 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

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