Memory correlation effect on thermal ratchets

We introduce correlation between steps in a random walk model with asymmetric piecewise linear potential where either a force or the barrier height fluctuates between two states. We call the correlation between steps that we introduce in the model memory correlation to distinguish it from the usual time correlation of the fluctuations on ratchets. The model gives a qualitative idea of the effect of finite inertia on thermal ratchets. The statistical measures that we have used to characterize the particle movement are the ratchet current and the temporal autocorrelation function. We find steady-state current reversals upon varying the memory effect parameter. We find also a transition in the autocorrelation function with increasing memory correlation that indicates a change from long memory correlated to randomly correlated motion.