Directed transport of two-coupled Brownian particles in a rough potential

Revealing transport behaviors of Brownian particles in rough potential is of great significance for understanding some physical and biological phenomena. We study the effect of roughness in the potential landscape on the transport of two coupled inertial Brownian particles subjected to a time-periodic force in a Gaussian environment. The transport property is characterized by the current, the time-averaged asymptotic velocity. The interactions, between the roughness and the coupling strength, the driving strength, noise, as well as the coupling length, lead to the transport particularly complex, such as the current varies non-monotonically with the coupling and/or the coupling length, the moderate roughness can enhance the transport but the large roughness can hinder the transport in the case of weak driving, and so on. The mechanism governing these processes is revealed by the effective potential and the corresponding effective driving. The most important finding is that the wells formed by the roughness act as a ladder for the coupled particles to climb up and over the side of the ratchet in some situations, while they serve as the traps to imprison the particles in other situations. These results perhaps can provide guidance for enhancing transport performance of the coupled particles in a rough environment.