Pulsating potential ratchet

We consider Brownian motion in a periodic array of potential wells. The potential barriers between adjacent wells are spatially symmetric and pulsating periodically in time. While the modulation amplitude is the same for all barriers, the spatial symmetry is broken by sequentially alternating the respective pulsation frequencies among three different incommensurate values. The result is a net motion (ratchet effect), whose direction depends in an intriguing way on the detailed choice of parameters