Spatiotemporal Characterization of Active Brownian Dynamics in Channels
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915857658019840 |
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| author | Baouche, Yanis Guéneau, Mathis Kurzthaler, Christina |
| author_facet | Baouche, Yanis Guéneau, Mathis Kurzthaler, Christina |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_12080 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spatiotemporal Characterization of Active Brownian Dynamics in Channels Baouche, Yanis Guéneau, Mathis Kurzthaler, Christina Statistical Mechanics Soft Condensed Matter Probability 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. |
| title | Spatiotemporal Characterization of Active Brownian Dynamics in Channels |
| topic | Statistical Mechanics Soft Condensed Matter Probability |
| url | https://arxiv.org/abs/2603.12080 |