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Two-dimensional active Brownian particles crossing a parabolic barrier: Transition-path times, survival probability, and first-passage time

Michele Caraglio*

  • *Contact author: michele.caraglio@uibk.ac.at
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Phys. Rev. E 112, 024136 – Published 26 August, 2025

DOI: https://doi.org/10.1103/pw94-4g1n

Abstract

We derive an analytical expression for the propagator and the transition path time distribution of a two-dimensional active Brownian particle crossing a parabolic barrier with absorbing boundary conditions at both sides. By taking those of a passive Brownian particle as basis states and dealing with the activity as a perturbation, our solution is expressed in terms of the perturbed eigenfunctions and eigenvalues of the associated Fokker-Planck equation once the latter is reduced by taking into account only the coordinate along the direction of the barrier and the self-propulsion angle. We show that transition path times are typically shortened by the self-propulsion of the particle. Our solution also allows us to obtain the survival probability and the first-passage times distribution, which display a strong dependence on the particle's activity, while the rotational diffusivity influences them to a minor extent.

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Phys. Rev. E 112, 024136– Published 26 August, 2025
  • Received 4 October 2024
  • Revised 8 July 2025
  • Accepted 6 August 2025
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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.

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