Transport coherence and diffusion in a temporal asymmetric rocked ratchet model

Abstract

We study the dynamics of an over damped Brownian particle in a saw tooth potential in the presence of a temporal asymmetric driving force. We observe that in the deterministic limit, the transport coherence, which is determined by a dimensionless quantity called Peclet number, P e is quite high for larger spatial asymmetry in the ratchet potential. For all the regime of parameter space of this model, P e follows the nature of current like Stokes efficiency. Diffusion as a function of amplitude of drive shows a minimum exactly at which the current shows a maximum. Unlike the previously studied models, the P e as a function of temperature shows a peaking behavior and the coherence in transport decreases for high temperatures. In the nonadiabatic regime, the P e as a function of amplitude of drive decreases and the peak gets broader as a result the transport becomes unreliable.

Velocity auto correlation function of a confined Brownian particle

“…We have considered the dynamics of a Brownian particle in an effective potential U (x, t) and in the presence of a linear velocity dependent force, f s (1 − v v0 ), with f s as constant and v 0 as the autonomous velocity of the particle, respectively [27]. The motion of the particle is governed by the Langevin equation of motion [37][38][39]…”