Transport Regimes of Underdamped Brownian Particles in a Tilted Washboard Potential

Abstract

In this paper, a comprehensive examination of the temperature- and bias-dependent diffusion regimes of underdamped Brownian particles is presented. A temperature threshold reminiscent of a phase transition between anomalous and normal diffusive behaviors is located. In the low temperature regime, the system exhibits an apparent negative differential mobility due to persistent, long-time subdiffusion at low-bias; at high temperature (or critical bias,) the system rapidly approaches normal diffusion below an intermediate barrier height, U0 ? 6kBT. By comparison of the underdamped and overdamped response, it is demonstrated that the non-monotonic temperature dependence of the diffusivity can be traced to inertial effects. The velocity power spectra exhibit coupling between the \locked and \running states in the giant diffusion regime, with a characteristic frequency corresponding to the principal frequency of the limit cycles of a damped, driven plane pendulum near critical bias. Non-linear second harmonic generation, corresponding to oscillatory transient anomalous diffusivity, is observed with increasing bias and decreasing temperature, further emphasizing that the low-noise diffusion problem converges to noise-free dynamics, complementing analytic results for the average velocity [L. Cheng and N.K. Yip, Physica D, 2015].