Strong Mobility in Weakly Disordered Systems

We study transport of interacting particles in weakly disordered media. Our one-dimensional system includes (i) disorder, the hopping rate governing the movement of a particle between two neighboring lattice sites is inhomogeneous, and (ii) hard core interaction, the maximum occupancy at each site is one particle. We find that over a substantial regime, the root-mean-square displacement of a particle $\sigma$ grows superdiffusively with time $t$, $\sigma \sim (ϵt{)}^{2/3}$, where $ϵ$ is the disorder strength. Without disorder the particle displacement is subdiffusive, $\sigma \sim t^{1/4}$, and therefore disorder strongly enhances particle mobility. We explain this effect using scaling arguments, and verify the theoretical predictions through numerical simulations. Also, the simulations show that regardless of disorder strength, disorder leads to stronger mobility over an intermediate time regime.

Figure 1

Illustration of the disordered interacting particle system. The arrows indicate the bias at each site, the circles indicate vacant sites, and the bullets indicate occupied sites.

Figure 2

The three regimes of behavior (5). The displacement $\sigma$ is plotted versus time $t$ using a double logarithmic scale.

Figure 3

The early and intermediate behaviors for weak disorder, $ϵ={10}^{-2}$ (bullets), and no disorder, $ϵ=0$ (squares). Shown is the displacement $\sigma$ versus time $t$ as well as a reference line with slope $2/3$. The inset shows that the scaled displacement $\sigma {ϵ}^{2/5}$ is a universal function of the scaled time $t{ϵ}^{8/5}$ using $ϵ=0.01$ (bullets) and $ϵ=0.003$ (squares).

Figure 4

The late time behavior for $ϵ={10}^{-1}$. Shown is the displacement $\sigma$ versus time $t$ for noninteracting particles (bullets) and for interacting particles (squares).

Figure 5

The displacement $\sigma$ versus time $t$ for interacting particles (main figure) and noninteracting particles (inset) without disorder ($ϵ=0$, squares) and with moderate disorder values of $ϵ=0.1$ (bullets), $ϵ=0.2$ (diamonds), $ϵ=0.3$ (up triangle), and $ϵ=0.4$ (down triangle).