Simulation of active Brownian particles in optical potentials

Optical forces can affect the motion of a Brownian particle. For example, optical tweezers use optical forces to trap a particle at a desirable position. Unlike passive Brownian particles, active Brownian particles, also known as microswimmers, propel themselves with directed motion and thus drive themselves out of equilibrium. Understanding their motion in a confined potential can provide insight into out-of-equilibrium phenomena associated with biological examples such as bacteria, as well as with artificial microswimmers. We discuss how to mathematically model their motion in an optical potential using a set of stochastic differential equations and how to numerically simulate it using the corresponding set of finite difference equations.