Analysis on the Origin of Directed Current from a Class of Microscopic Chaotic Fluctuations - CHEW, L. Y. (Institutional Knowledge at Singapore Management University, 2004)
We show that the Perron-Frobenius equation of microscopic chaos based on double symmetric maps leads to an inhomogeneous Smoluchowski equation with a source term. Our perturbative analysis reveals that the source term gives rise to a directed current for a strongly damped particle in a spatially periodic potential. In addition, our result proves that in the zeroth-order limit, the position distribution of the particle obeys the Smoluchowski equation even though the fluctuating force is deterministic.