Steady-state currents in sharp stochastic ratchets

We develop and analyze a model for particle transport in a stochastic ratchet with a periodic piecewise linear potential, with diffusion coefficient D, where the force is discontinuous in position and fluctuating in time via additive telegraph noise with correlation time tau. We find asymptotic formulas for the steady-state particle current J for large and small D and tau. For example, for small tau, the sharp corners in the potential lead to J=O(tau(2) exp[-(Dtau)(-1/2)])+O(tau(5/2)), in contrast to O(tau(3)) when the potential is smooth. We show that diffusion can increase or decrease J, and derive an approximate equation for the value of D that maximizes J.