Critical hysteresis in a tilted washboard potential

The Brownian motion in a tilted washboard potential subjected to a low-freq uency periodic drive develops large hysteresis loops, which attain their ma ximum at the locked-to-running transition in the underdamped regime. The de pendence of such a critical phenomenon on the drive parameters and on the t emperature is investigated numerically. Moreover, this hysteresis mechanism is related to the occurrence of random multiple jumps, whose length and ti me duration distributions appear to decay according to a universal power la w with exponent alpha = 1.5. This model may explain various instances of lo w-frequency excess damping in material science. [S0031-9007(99)08872-9].