Stochastic dynamics of an active particle escaping from a potential well

Active matter systems are driven out of equilibrium by the energy directly supplied at the level of constituent active particles that are self-propelled. We consider a model for an active particle in a potential well, characterized by an active velocity with a constant magnitude but a random orientation subject to white noises. We are interested in the escape of the active particle from the potential well in multiple-dimensional space. We investigate two distinct optimal paths, namely, the shortest arrival-time path and the most probable path, by using the analytical and numerical techniques from optimal control and rare event modeling. In particular, we elucidate the relationship between these optimal paths and the reachable set using the Hamiltonian dynamics for the shortest arrival-time path and the geometric minimum action method for the most probable path, respectively. Numerical results are presented by applying these techniques to a two-dimensional double-well potential.