Transport coefficients for a confined Brownian ratchet operating between two heat reservoirs

TL;DR

This paper investigates the transport properties of a Brownian particle in a confined, asymmetric channel with different noise intensities, deriving analytical expressions for velocity and diffusion that are validated numerically.

Contribution

It introduces a model combining Fick-Jacobs approximation with asymmetric channels and different temperatures, providing exact results for small widths and qualitative insights for larger ones.

Findings

Derived mean velocity and diffusion coefficient using Fick-Jacobs approximation.

Validated analytical results with numerical calculations across channel widths.

Confirmed ratchet effect persists beyond small channel width approximation.

Abstract

We discuss two-dimensional diffusion of a Brownian particle confined to a periodic asymmetric channel with soft walls modeled by a parabolic potential. In the channel, the particle experiences different noise intensities, or temperatures, in the transversal and longitudinal directions. The model is inspired by the famous Feynman's ratchet and pawl. Using ideas of the Fick-Jacobs approximation we derive the mean velocity of the particle, the effective diffusion coefficient, and the stationary probability density in the potential unit cell. The derived results are exact for small channel width. Yet, we check by exact numerical calculation that they qualitatively describe the ratchet effect observed for an arbitrary width of the channel.