Diffusion of Brownian particles in a tilted periodic potential under the influence of an external Ornstein–Uhlenbeck noise

Highlights: • A nonmonotonic dependence of diffusion coefficient on correlation time is found. • A physical mechanism beyond locked-to-running transition is proposed. • Some abnormal diffusive behaviors for small noise intensities are found and studied. • Rich simulation results are presented and the physical mechanisms are explored. - Abstract: The diffusion behaviors of Brownian particles in a tilted periodic potential under the influence of an internal white noise and an external Ornstein–Uhlenbeck noise are investigated through numerical simulation. In contrast to the case when the bias force is smaller or absent, the diffusion coefficient exhibits a nonmonotonic dependence on the correlation time of the external noise when bias force is large. A mechanism different from locked-to-running transition theory is presented for the diffusion enhancement by a bias force in intermediate to large damping. In the underdamped regime and the presence of external noise, the diffusion coefficient is a monotonically decreasing function of low temperature rather than a nonmonotonic function when external noise is absent. The diffusive process undergoes four regimes when bias force approaches but is less than its critical value and noises intensities are small. These behaviors can be attributed to the locked-to-running transition of particles.