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Transport coherence in a time-asymmetric rocked ratchet model

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, $Pe$ is quite high for larger spatial asymmetry in the ratchet potential. For all the regime of parameter space of this model, $Pe$ 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 $Pe$ as a function of temperature shows a peaking behavior and the coherence in transport decreases for high temperatures. In the nonadiabatic regime, the $Pe$ as a function of amplitude of drive decreases and the peak gets broader as a result the transport becomes unreliable.