The effects of roughness of the periodic substrate potential on anomalous mobility

We investigate the anomalous mobility and diffusion of an inertial Brownian particle moving in a rough periodic substrate potential subjected to a time-periodic force and external bias in a Gaussian colored noise environment. Drawing on prior research, we discover that for the deterministic case, roughness is also an effective factor for controlling absolute negative mobility in addition to the shape parameter of the potential and external forces. And the phase space map and bifurcation diagram are utilized to evaluate the observations. In the presence of Gaussian colored noise, roughness can result in coexistence of absolute negative mobility and anomalous diffusion. It is discovered that small amplitude roughness causes negative mobility, whereas large amplitude roughness can weaken or even eliminate it. In the weak noise limit, roughness may enhance or hinder mobility, nevertheless, in the moderate to strong noise limit, roughness leads to an increase in directed transport. Moreover, it is of vital significance that the moderate roughness induces enhanced stability of system, resonant-like activation and anomalous diffusion, whereas larger roughness may cause the disappearance of diffusion. Our results have practicability for further studies of anomalous transport of particles and designs of various devices, such as hydrogen-bonded networks, superconducting nanowires, and crystals with dislocations.