Active Brownian Dynamics in Channels: First-Passage and Spatiotemporal Properties via Siegmund Duality
Year: 2026
Type: article
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.
Source: Physical Review Letters
DOI: 10.1103/g83n-r4hs
Language: English
Topic: Micro and Nano Robotics
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,750
OpenAlex ID: W7204090539