The steady current analysis in a periodic channel driven by correlated noises

A system consisting of correlated noises and a channel is analyzed. Via the Fick-Jacobs equation for the system's current evolution, the validity are discussed under three kinds of correlated noise. i) The first case is two Gaussian white noises with a white correlation. We found that in contrast to the single white noise, the white correlation between these two noises breaks the system's symmetry and causes a directed current and the larger the correlation degree, the smaller the current. However, the interaction between the correlation degree and a sinusoidal potential may produce an increasing steady current. ii) The second one is two Gaussian white noises with an exponential correlation. And our results perform that the correlation time between them contributes to a decrease of the steady current. iii) Finally, the case that two Gaussian colored noises with an exponential correlation is investigated. Unlike the former two cases, whether the correlation time comes from the noise itself or the correlation between the two noises, its increase here can always cause an increasing current.