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

Yuanyuan Jiao, Fengzao Yang, Chunhua Zeng*

Abstract: 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.