Driven classical diffusion with strong correlated disorder

For driven classical diffusion quenched by a strong potential disorder $V\left(x\right)$, we identify a prominent crossover regime between the regimes of very small and very large driving forces $F$, where the corresponding mobility values $\mu \left(F\right)$ differ exponentially. For disorder with power-law correlations at large distances $⟨V\left(x\right)V\left(y\right)⟩\sim {\mid x-y\mid }^{-n},n>0$, the crossover is characterized by power-law dependence of the logarithm of $\mu \left(F\right)$ on the driving force $\ln \mu \left(F\right)\sim F^{n∕(n+1)}$. For finite-range disorder (formally, $n=\infty$), the corresponding dependence is linear (“logarithmic susceptibility”).

Figure 1

(Color online) Logarithm of the effective mobility renormalization $\ln \mathbf{(}\mu \left(F\right)∕\mu \left(0\right)\mathbf{)}$ [Eqs. (6, 7)] with the correlation function $g\left(x\right)={(1+x^2∕{\xi }_1^2)}^{-n∕2}$ for strong disorder $(V_0∕T=5)$ and large driving forces $F$. Dotted lines guide the eye with the slope of the intermediate asymptote (14). The thin solid line is the analytic result (15) for $n=1$.

Figure 2

(Color online) As in Fig. 1 but for small driving forces $F$. Thin solid lines indicate the nonlinear correction calculated analytically: linear in $F$ for $n>1$, proportional to $F^n$ for $n<1$, and Eq. (15) for $n=1$.