Regular and Chaotic Transport in Asymmetric Periodic Potentials: Inertia Ratchets

Motivated by recent work on stochastic ratchets, we consider the effect of finite inertia onto the directed motion in a deterministically rocked, periodic potential lacking reflection symmetry. Characterizing the motion by cumulants of the contracted, time-dependent solution of the Liouville equation, we can distinguish regular from chaotic transport. The first cumulant describes a stationary current that exhibits multiple reversals versus increasing driving strength, whereas the second cumulant yields a measure for its variance. Chaotic transport exhibits universal (Gaussian) scaling behavior.