Role of phase difference and colored cross-correlation on current in multiplicative and additive noises driven systems

We have investigated the transport properties of multiplicative and additive noise driven spatially periodic system. The phase difference between periodic potential and periodic function in multiplicative noise term and the cross-correlation between multiplicative and additive noise can break the detail balance of the system independently to produce directed motion. The magnitude of current due to phase difference is smaller in comparison to cross-correlation between the noises. The phase difference can be used to control the direction of the cross-correlation induced current. Another interesting observation is that there is a current inversion with increase of cross-correlation time (τ)(τ). The current increases linearly with the strength of cross-correlation.