Orientational Distribution of an Active Brownian Particle: an analytical study

Supurna Sinha

Published 2020-03-23Version 1

We use the Fokker Planck equation as a starting point for studying the orientational probability distribution of an Active Brownian Particle (ABP) in $(d+1)$ dimensions. This Fokker Planck equation admits an exact solution in series form which is, however, unwieldly to use because of poor convergence for short and intermediate times. We present an analytical closed form expression, which gives a good approximate orientational probability distribution. The analytical formula is derived using saddle point methods for short times. However, it works well even for intermediate times. %We expect this approximate formula to lead to an efficient algorithm for integration of the dynamics of an ABP. Our predictions can be tested against future experiments and simulations probing orientational probability distribution of an ABP.