Particle Distribution Law Induced by Colored Noise in a Bistable Potential Field: A Counterintuitive Trimodal Distribution

This paper investigates the non-equilibrium transport of particles crossing over the potential barrier in a bistable potential field driven by colored noise, and the most astonishing thing is that there exists a counter-intuitive phenomenon, the third steady state besides the normal bimodal distribution. The model, the Langevin equation , is analyzed by being transformed into the Fokker-Planck equation, and the time-dependent solution is obtained via conducting the Fourier transform. The regulatory effects of potential landscape parameter, the memory duration and intensity of the noise on the particle distribution are systematically unveiled through the calculations of the mean first passage time, diffusion coefficient, effective potential, and the spatial correlation as well. The results indicate that under a specific potential landscape, the system after a long-term evolution exhibits a trimodal distribution. The third peak is located on the right half slope of the potential barrier, which implies that colored noise induces the third steady state beyond the bistable ones. The effective potential that takes into account the contribution of colored noise reveals the influence of the noise on the particle movement/position. The spatial correlation plays a key role in enabling the particles to cross the potential barrier against the gradient force of the potential field, determining the peak position of the distribution to deviate from the bottom of the potential field, and stabilizing the third peak near the top of the potential barrier. Short-memory noise can significantly shorten the mean first passage Yuan-Rui Wang et al. time, while long-memory noise triggers a transition of the sub-diffusion to the super-diffusion. These counter-intuitive phenomena provide new insights for the control of multi-steady states and the optimization of transport in nonlinear systems.