Critical Hysteresis in a Tilted Washboard Potential

The Brownian motion in a tilted washboard potential subjected to a low-frequency periodic drive develops large hysteresis loops, which attain their maximum at the locked-to-running transition in the underdamped regime. The dependence of such a critical phenomenon on the drive parameters and on the temperature is investigated numerically. Moreover, this hysteresis mechanism is related to the occurrence of random multiple jumps, whose length and time duration distributions appear to decay according to a universal power law with exponent $\alpha =1.5\mathrm{}$. This model may explain various instances of low-frequency excess damping in material science.