Absolute transverse mobility and ratchet effect on periodic two-dimensional symmetric substrates

We present a simple model of an overdamped particle moving on a two-dimensional symmetric periodic substrate with a dc drive in the longitudinal direction and additional ac drives in both the longitudinal and transverse directions. For certain regimes we find that a finite longitudinal dc force produces a net dc response only in the transverse direction, which we term absolute transverse mobility. Additionally, we find regimes exhibiting a ratchet effect in the absence of an applied dc drive.