Biased transportations in a spatially asymmetric system at the nano-scale under thermal noise

Under the theory of ratchet effect for mesoand macro-scale systems, the additional perturbation with a long time correlation and the breaking of spatial inversion symmetry are two main ingredients to bring unidirected transportations. With the help of a simple model system, we show that a spatially asymmetric system of the nano-scale length may induce biased transportations under thermal noise.