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

[2603.12080] Active Brownian Dynamics in Channels: First-Passage and Spatiotemporal Properties via Siegmund Duality Skip to main content Search Submit Donate Log in Condensed Matter > Statistical Mechanics arXiv:2603.12080 (cond-mat) [Submitted on 12 Mar 2026 ( v1 ), last revised 25 Aug 2026 (this version, v2)] Title: Active Brownian Dynamics in Channels: First-Passage and Spatiotemporal Properties via Siegmund Duality Authors: Yanis Baouche , Mathis Guéneau , Christina Kurzthaler View PDF HTML (experimental) 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. Comments: 10 pages, 4 figures Subjects: Statistical Mechanics (cond-mat.stat-mech) ; Soft Condensed Matter (cond-mat.soft); Probability (math.PR) Cite as: arXiv:2603.12080 [cond-mat.stat-mech] (or arXiv:2603.12080v2 [cond-mat.stat-mech] for this version) https://doi.org/10.48550/arXiv.2603.12080 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Phys. Rev. Lett. 137, 138301 (2026) Related DOI : https://doi.org/10.1103/g83n-r4hs Focus to learn more DOI(s) linking to related resources Submission history From: Mathis Guéneau [ view email ] [v1] Thu, 12 Mar 2026 15:50:02 UTC (470 KB) [v2] Tue, 25 Aug 2026 07:24:01 UTC (656 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: cond-mat.stat-mech < prev | next > new | recent | 2026-03 Change to browse by: cond-mat cond-mat.soft math math.PR References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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