Combining geometrical and dynamical disorder to enhance transport

We look for the optimal way to distribute rectifiers in order to maximize their effect on the transport properties of Brownian particles. These rectifiers are introduced in the form of flashing asymmetric potentials distributed on a one dimensional lattice. We study the effects that different distributions of these rectifiers have on the generated current and on the energy cost of transport. Based on both analytical and numerical results, we observe an unexpected increase in the efficiency of the rectifiers and the magnitude of the current for the case in which geometrical and dynamical disorder are combined. We show that this effect is a direct consequence of the “hitchhiker” or “waiting time” paradox.

Figure 1

Two Ehrlich-Schwoebel potentials confining Brownian particles within a cell. The hopping probabilities are indicated over the arrows.

Figure 2

Schematic representation of the time evolution for the different scenarios used in this paper. “Normal” symmetric potentials replace the ES potentials for one unit of time after every $\tau -1$ units of time. In this figure, the concentration of rectifiers is $c=0.2$ for the periodic and temporal scenarios, yielding a spatial period $l=5$.

Figure 3

Results from Monte Carlo simulations for the different scenarios. We have plotted the average particle current $\left(J\right)$ vs the period $\left(\tau \right)$ for a concentration of ES potentials $c=0.2$.

Figure 4

Comparison between analytical results using Eqs. (7) (solid lines) and Monte Carlo simulations (dots). We have plotted the average current $J$ vs $\tau$ for a concentration of ES potentials $c=0.2$.

Figure 5

The efficiency per load $\epsilon$ vs $\tau$ for a concentration of ES potentials $c=0.2$. Units of energy are such that the depth of the ES wells is $\Delta V=1$.