Current reversals in ratchets driven by trichotomous noise

Abstract

The colored three-level Markovian noise-driven nonequilibrium dynamics of overdamped Brownian particles in a spatially periodic asymmetric potential (ratchet) is investigated. An explicit second-order linear ordinary differential equation for the stationary probability density distribution is obtained for the process. In the case of a piecewise linear potential with an additive three-level (trichotomous) noise the exact formula for the stationary current is presented. The dependence of the current reversals on the noise parameters is investigated in detail and illustrated by a phase diagram. Asymptotic formulas for the current for various limits of the noise parameters are found and compared with the results of other authors. Applications to the fluctuation-induced separation of particles are also discussed.

Facilitated movement of inertial Brownian motors driven by a load under an asymmetric potential

“…The Brownian particle changes its direction three times for ∆ = 0.05. It must be pointed out that multiple current reversals can be detected in overdamped Brownian systems driven by the colored three-level Markovian noises [15].…”

Absolute negative mobility in a one-dimensional overdamped system

“…(5), (6) and (8) then using the conditions of current continuum, periodic boundary and normalization, we can obtain the exact expressions of the current [34] …”

Comment on ‘Absolute negative mobility in a one-dimensional overdamped system’

“…Noise ξ(t) = {−a 0 , 0, a 0 } is a three-state stationary Markov process. The stationary probabilities are [2] P s (−a 0 ) = P s (a 0 ) = q, P s (0) = 1 − 2q, 0 < q < 1/2. The transition probabilities per unit time between these states are given by the relations…”