First-passage-time statistics of active Brownian particles: A perturbative approach

Area of Science:

• Physics
• Statistical Mechanics
• Soft Matter Physics

Background:

• Active Brownian particles (ABPs) exhibit self-propelled motion, differing from passive Brownian counterparts.
• First-passage-time (FPT) is a critical parameter in understanding particle dynamics and system behavior.
• The Péclet number quantifies the ratio of self-propulsion to diffusion in active matter systems.

Purpose of the Study:

• To investigate the first-passage-time properties of active Brownian particles approaching an absorbing wall in a 2D environment.
• To derive exact analytical predictions for survival and FPT distributions for small Péclet numbers.
• To quantify the role of initial orientation on FPT statistics and identify conditions where anisotropy is pronounced.

Main Methods:

• Utilizing a perturbation approach to derive analytical solutions.
• Calculating survival and first-passage-time distributions.
• Employing the median as a metric to quantify the anisotropy in FPT.

Main Results:

• Active Brownian particles generally reach the absorbing wall faster than passive particles.
• The initial orientation of active agents critically influences the first-passage-time distributions.
• Anisotropy in FPT becomes more pronounced at larger distances where active motion dominates diffusion.

Conclusions:

• The self-propulsion of active Brownian particles significantly alters their FPT behavior compared to passive particles.
• Initial orientation is a key factor in determining the speed and statistics of wall approach.
• The study provides exact analytical predictions for low Péclet numbers, offering insights into active matter dynamics.