Diffusion and Current of Brownian Particles in Tilted Piecewise Linear Potentials: Amplification and Coherence

TL;DR

This paper derives explicit formulas for diffusion, current, and coherence of overdamped Brownian particles in tilted piecewise linear potentials, analyzing their dependence on system parameters and revealing conditions for non-monotonic diffusion behavior.

Contribution

It provides new algebraic expressions and analysis for diffusion and coherence in tilted periodic potentials, highlighting sensitivity to potential asymmetry and conditions for diffusion amplification.

Findings

Diffusion coefficient and coherence are highly sensitive to potential asymmetry.

Non-monotonic diffusion behavior depends on temperature and external force.

Enhanced diffusion occurs with a wide coherence plateau at low temperatures.

Abstract

Overdamped motion of Brownian particles in tilted piecewise linear periodic potentials is considered. Explicit algebraic expressions for the diffusion coefficient, current, and coherence level of Brownian transport are derived. Their dependencies on temperature, tilting force, and the shape of the potential are analyzed. The necessary and sufficient conditions for the non-monotonic behavior of the diffusion coefficient as a function of temperature are determined. The diffusion coefficient and coherence level are found to be extremely sensitive to the asymmetry of the potential. It is established that at the values of the external force, for which the enhancement of diffusion is most rapid, the level of coherence has a wide plateau at low temperatures with the value of the Peclet factor 2. An interpretation of the amplification of diffusion in comparison with free thermal diffusion in terms of probability distribution is proposed.