Drift by Dichotomous Markov Noise

TL;DR

This paper derives explicit formulas for the long-term probability density and drift velocity in systems influenced by dichotomous Markov noise, especially when crossing unstable fixed points, with applications to rocking ratchets.

Contribution

It provides new explicit results for asymptotic behavior in systems driven by dichotomous Markov noise, including unstable fixed point crossings.

Findings

Explicit formulas for asymptotic probability density.

Explicit formulas for drift velocity.

Application to rocking ratchet problem.

Abstract

We derive explicit results for the asymptotic probability density and drift velocity in systems driven by dichotomous Markov noise, including the situation in which the asymptotic dynamics crosses {\em unstable} fixed points. The results are illustrated on the problem of the rocking ratchet.