A minimal deterministic model of Brownian motors

We analyze the chaotic diffusion of Brownian particles in a periodic array of deterministically coupled maps. For certain values of its two control parameters the model we study is reminiscent of a simple random walk on the line, however, there is always an infinite memory in the particle dynamics. This enables to study whether microscopic dynamical correlations can play a role in Brownian motion. We first show that our model is a time-discrete version of the dynamics of Brownian particles in asymmetric periodic potentials under the impact of a periodic force. We then exactly calculate the drift and diffusion coefficients for our model. We find that there exist current reversals under parameter variation, as is well-known for Brownian motors. We argue that these current reversals are due to microscopic correlations in the particle dynamics.