  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. 
Absolute Transverse Mobility and Ratchet Effect on Periodic 2D Symmetric   Substrates