title: Minimal Brownian ratchet: an exactly solvable model.
abstract: We develop an analytically solvable three-state discrete-time minimal Brownian ratchet (MBR), where the transition probabilities between states are asymmetric. By solving the master equations, we obtain the steady-state probabilities. Generally, the steady-state solution does not display detailed balance, giving rise to an induced directional motion in the MBR. For a reduced two-dimensional parameter space, we find the null curve on which the net current vanishes and detailed balance holds. A system on this curve is said to be balanced. On the null curve, an additional source of external random noise is introduced to show that a directional motion can be induced under the zero overall driving force.
authors.affiliation: Yanbian University of Science & Technology, Beishan St. Yanji, Jilin 133000, China.
authors.forename: Youngki
authors.initials: Y
authors.lastname: Lee
authors.forename: Andrew
authors.initials: A
authors.lastname: Allison
authors.forename: Derek
authors.initials: D
authors.lastname: Abbott
authors.forename: H Eugene
authors.initials: HE
authors.lastname: Stanley