Ratchet effect in inhomogeneous inertial systems: I. Adiabatic case

TL;DR

This paper investigates how spatially varying friction influences the ratchet effect in inertial systems under adiabatic conditions, revealing complex behaviors and dependencies on force, temperature, and friction parameters.

Contribution

It introduces a detailed analysis of the ratchet current in inhomogeneous inertial systems using Risken's matrix continued fraction method, highlighting the effects of frictional inhomogeneity.

Findings

Ratchet current exhibits rich qualitative behaviors despite weak frictional inhomogeneity.

Current depends on force, temperature, and average friction coefficient.

Inhomogeneous friction can induce directed transport in symmetric potentials.

Abstract

Risken's matrix continued fraction method is used to solve the Fokker-Planck equation to calculate particle current in an inertial symmetric (sinusoidal) periodic potential under the action of a constant force. The particle moves in a medium with friction coefficient also varying periodically in space as the potential but with a finite phase difference $\phi (\ne n\pi, n=0,1,2, ...)$. The algebraic sum of current with applied forces $\pm|F|$ gives the ratchet current in the adiabatic limit. Even though, the effect of frictional inhomogeneity is weak, the ratchet current shows very rich qualitative characteristics. The effects of variation of $F$, the temperature $T$, and the average friction coefficient $\gamma_0$ on the performance characteristics of the ratchet are presented.