Active Brownian particles in a circular disk with an absorbing boundary.

Area of Science:

• Statistical Mechanics
• Soft Matter Physics
• Nonlinear Dynamics

Background:

• Brownian motion describes particle diffusion.
• Active Brownian particles exhibit self-propulsion.
• Absorbing boundaries model particle loss.

Purpose of the Study:

• Solve the time-dependent Fokker-Planck equation for a 2D active Brownian particle.
• Analyze the impact of particle activity and rotational diffusivity on dynamics near an absorbing boundary.
• Obtain survival probability and first-passage time distributions.

Main Methods:

• Matrix representation of the Fokker-Planck operator using passive Brownian particles as basis states.
• Perturbation theory to account for particle activity.
• Expressing the propagator using perturbed eigenvalues and eigenfunctions.
• Alternative representation using equilibrium eigenstates and iterative relations.

Main Results:

• The propagator is derived using a matrix method and perturbation theory.
• Survival probability and first-passage time distributions are obtained.
• These distributions show unique behavior due to nonequilibrium dynamics.
• Strong dependence on particle activity and moderate dependence on rotational diffusivity observed.

Conclusions:

• The developed analytical solution accurately describes active Brownian particle dynamics near an absorbing boundary.
• Nonequilibrium effects significantly alter escape and survival probabilities.
• The findings provide insights into active matter behavior in confined environments.