Transport and time-dependent diffusion of inertial Brownian particle in tri-stable potential

In this paper, we investigate the transport and time-dependent diffusion properties of inertial Brownian particles in a one-dimensional symmetric tri-stable potential driven by correlation between multiplicative and additive noises. The effects of multiplicative and additive noises, and correlation between noises on the transport and time-dependent diffusion of the IBPs is discussed, respectively. Research results show that: (i) the correlation between noises can generate a net velocity, and its physical mechanism may be that the correlation between noises can induce state transition phenomenon; (ii) with the increase in the absolute value of the correlation strength, the mean velocity increases, while the diffusion decreases; and (iii) the mean velocity exhibits a strong nonmonotonic dependence on the multiplicative and additive noises, we also study time-dependent diffusions corresponding to these transports and find that the system has the phenomenon of coexistence of superdiffusion and subdiffusion (i.e., abnormal diffusion) in different time intervals, and superdiffusion and subdiffusion can be induced by manipulating these noises. Our research may help to further understand the self-propelled motion of biological processes, not least understanding the transport properties occurring in different stages of a biological process.