Deterministic inhomogeneous inertia ratchets

TL;DR

This paper investigates how spatially varying friction in a symmetric periodic potential can induce directed motion in a driven particle, highlighting the roles of inhomogeneity, initial phase averaging, and noise in ratchet dynamics.

Contribution

It demonstrates that frictional inhomogeneity can mimic asymmetry effects in deterministic ratchets and emphasizes the importance of initial phase averaging and noise in current generation.

Findings

Frictional inhomogeneity reproduces features of asymmetric potentials.

Averaging over initial phase is crucial at low inhomogeneity.

Noise enables ratchet current at low drive amplitudes.

Abstract

We study the deterministic dynamics of a periodically driven particle in the underdamped case in a spatially symmetric periodic potential. The system is subjected to a space-dependent friction coefficient, which is similarly periodic as the potential but with a phase difference. We observe that frictional inhomogeneity in a symmetric periodic potential mimics most of the qualitative features of deterministic dynamics in a homogeneous system with an asymmetric periodic potential. We point out the need of averaging over the initial phase of the external drive at small frictional inhomogeneity parameter values or analogously low potential asymmetry regimes in obtaining ratchet current. We also show that at low amplitudes of the drive, where ratchet current is not possible in the deterministic case, noise plays a significant role in realizing ratchet current.