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arXiv · 2410.07226

Two-Dimensional Active Brownian Particles Crossing a Parabolic Barrier: Finite Rectangular Domain with Absorbing Boundary Conditions

Michele Caraglio
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Abstract

We solve the time-dependent Fokker-Planck equation for a two-dimensional active Brownian particle exploring a rectangular domain with absorbing boundary and in the presence of a parabolic barrier along one direction. By taking those of a passive Brownian particle as basis states and dealing with the activity as a perturbation, we provide a matrix representation of the Fokker-Planck operator and express the propagator in terms of the perturbed eigenvalues and eigenfunctions. Our solution also allows us to obtain the survival probability and the first-passage-time distribution. The non-equilibrium character of the dynamics induces a strong dependence of the latter quantities on the particle's activity, while the rotational diffusivity influences them to a minor extent.

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Michele Caraglio. 2024-10-02. Two-Dimensional Active Brownian Particles Crossing a Parabolic Barrier: Finite Rectangular Domain with Absorbing Boundary Conditions. https://doi.org/10.1088/1742-5468%2Fae38d2

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