Escape rate of an active Brownian particle in a rough potential

We discuss the escape problem with the consideration of both the activity of particles and the roughness of potentials. We derive analytic expressions for the escape rate of an active Brownian particle in two types of rough potentials by employing the effective equilibrium approach and the Zwanzig method. We find that activity enhances the escape rate, but both the oscillating perturbation and the random amplitude hinder escaping.