Abstract
Hopping conductivity is considered in a one-dimensional (1D) system with a finite density of impurities which present a finite barrier to hopping. The nonlinear hopping equations, which exclude jumps to occupied sites, are solved for steady-current conditions in an applied electric field $E$. The current saturates at a value independent of $E$ and of $c$ for $c\ensuremath{\lesssim}\frac{\mathrm{eaE}}{{k}_{B}T}\ensuremath{\ll}1$ where $c$ is the impurity concentration and $a$ the lattice spacing.
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