Rectification of confined diffusion driven by a sinusoidal force.

A particle diffusing in an asymmetric periodic channel, driven by a sinusoidal force F(t)=F0cosωt (the rocking ratchet) is considered. The asymptotic solution of the generalized Fick-Jacobs equation describing the system is studied in the nonadiabatic regime. The leading term of the rectified current, appearing in the order ∼F02, is derived. The method presented enables us to solve the problem analytically for a sawtooth channel and also to look for approximative formulas applicable in a wide range of frequencies ω. Even the simplest approximation qualitatively reproduces the current reversal at higher frequencies as the result of growing phase lag of the rocking density behind the driving force.