Transport Regimes of Underdamped Brownian Particles in aTilted Washboard Potential

In this work, a Runge-Kutta numerical solution to the Langevin equation is computed for a tilted washboard potential. The parameter-space of temperature, tilt, and well-depth is analyzed for underdamped Brownian diffusion through the potential. In addition to the known non-monotonic temperature response of the diffusivity, we observe a negative differential mobility due to an overall decrease in jump rate and corresponding to a regime of anomalous diffusion. A new phase diagram is obtained, corresponding to a transition between sub-diffusion and normal diffusion as temperature approaches the intermediate barrier height, . Lifson-Jackson calculations of diffusivity’s monotonic temperature response for overdamped particles are contrasted with the nonmonotonic response of the underdamped system, highlighting the importance of inertia in the system dynamics. The zero-temperature dynamics are then analyzed through a bifurcation diagram, mimicking the dynamics of a damped, driven pendulum. Velocity power spectra reveal second harmonic generation corresponding to multistable particle dynamics and the dynamics converges to the zero-temperature limit for the instantaneous velocity, complementing the results for average velocity as shown by Cheng and Yip.