Diffusion Properties of a Brownian Ratchet with Coulomb Friction

TL;DR

This paper investigates how Coulomb friction influences the diffusion and directed motion of a Brownian particle in an asymmetric potential, revealing complex behaviors and regime transitions driven by non-linear friction effects.

Contribution

It provides a detailed analysis of Coulomb friction's impact on Brownian ratchet dynamics, including non-monotonic velocity behavior and regime transitions, with comparisons to linear models.

Findings

Stationary velocity exhibits non-monotonic dependence on temperature and viscosity.

Diffusion shows multiple distinct time regimes influenced by Coulomb friction.

Passage times between regimes are significantly affected by non-linear friction effects.

Abstract

The motion of a Brownian particle in the presence of Coulomb friction and an asymmetric spatial potential was evaluated in this study. The system exhibits a ratchet effect, i.e., an average directed motion even in the absence of an external force, induced by the coupling of non-equilibrium conditions with the spatial asymmetry. Both the average motion and the fluctuations of the Brownian particle were analysed. The stationary velocity shows a non-monotonic behaviour as a function of both the temperature and the viscosity of the bath. The diffusion properties of the particle, which show several time regimes, were also investigated. To highlight the role of non-linear friction in the dynamics, a comparison is presented with a linear model of a Brownian particle driven by a constant external force, which allows for analytical treatment. In particular, the study unveils that the passage times between different temporal regimes are strongly affected by the presence of Coulomb friction.