Active Brownian Particles in a Circular Disk with an Absorbing Boundary

Abstract

We solve the time-dependent Fokker-Planck equation for a two-dimensional active Brownian particle exploring a circular region with an absorbing boundary. Using the 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 we express the propagator in terms of the perturbed eigenvalues and eigenfunctions. Alternatively, we show that the propagator can be expressed as a combination of the equilibrium eigenstates with weights depending only on time and on the initial conditions, and obeying exact iterative relations. Our solution allows also obtaining the survival probability and the first-passage time distribution. These latter quantities exhibit peculiarities induced by the non-equilibrium character of the dynamics, in particular, they display a strong dependence on the activity of the particle and, to a less extent, also on its rotational diffusivity.

arXiv comment11pages, 6 figures

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• Large deviations in statistics of the convex hull of passive and active particles: A theoretical study
• Mean first passage time of active Brownian particles in two dimensions
• Elastic interactions compete with persistent cell motility to drive durotaxis
• Target search by active particles
• Concentration of Empirical First-Passage Times
• Two-Dimensional Active Brownian Particles Crossing a Parabolic Barrier: Finite Rectangular Domain with Absorbing Boundary Conditions
• Two-Dimensional Active Brownian Particles Crossing a Parabolic Barrier: Transition-Path Times, Survival Probability, and First-Passage Time