Ratchet effect in inhomogeneous inertial systems: II. The square-wave drive case

TL;DR

This study numerically investigates a particle in an inhomogeneous inertial system under a symmetric square-wave drive, revealing steady ratchet currents, peaking diffusion coefficients, and complex dispersion behaviors at various time scales.

Contribution

It provides a detailed numerical analysis of ratchet effects in inhomogeneous inertial systems driven by square waves, highlighting new behaviors in steady current and diffusion.

Findings

Ratchet current peaks at specific forcing amplitudes.

Diffusion coefficient shows peaking behavior near the current peak.

System exhibits complex dispersion regimes affecting current.

Abstract

The underdamped Langevin equation of motion of a particle, in a symmetric periodic potential and subjected to a symmetric periodic forcing with mean zero over a period, with nonuniform friction, is solved numerically. The particle is shown to acquire a steady state mean velocity at asymptotically large time scales. This net particle velocity or the ratchet current is obtained in a range of forcing amplitudes $F_0$ and peaks at some value of $F_0$ within the range depending on the value of the average friction coefficient and temperature of the medium. At these large time scales the position dispersion grows proportionally with time, $t$, allowing for calculating the steady state diffusion coefficient $D$ which, interestingly, shows a peaking behaviour around the same $F_0$. The ratchet current, however, turns out to be largely coherent. At intermediate time scales, which bridge the small time scale behaviour of dispersion$\sim t^2$ to the large time one, the system shows, in some cases, periodic oscillation between dispersionless and steeply growing dispersion depending on the frequency of the forcing. The contribution of these different dispersion regimes to ratchet current is analysed.