Motional dispersions and ratchet effect in inertial systems

TL;DR

This paper investigates how inertial systems with symmetric potentials can exhibit a ratchet effect due to nonuniform friction, analyzing the phenomenon through analytical and numerical methods across different driving conditions.

Contribution

It introduces a novel mechanism for ratchet effects in inertial systems driven by symmetric forces, emphasizing the role of nonuniform friction and extending analysis to finite-frequency drives.

Findings

Ratchet effect occurs in symmetric potentials with nonuniform friction.

Dispersionless behavior observed in transient time scales.

Complex dispersion behavior under periodic drive.

Abstract

We obtain ratchet effect in inertial structureless systems in symmetric periodic potentials where the asymmetry comes from the nonuniform friction offered by the medium and driven by symmetric periodic forces. In the adiabatic limit the calculations are done by extending the matrix continued fraction method and also by numerically solving the appropriate Langevin equation. For finite frequency field drive the ratchet effect is obtained only numerically. In the transient time scales the system shows dispersionless behaviour as reported earlier when a constant force is applied. In the periodic drive case the dispersion behaviour is more complex. In this brief communication we report some of the results of our work