Hopping Conductivity in One Dimension

An asymptotic upper bound at low temperatures $\sigma \propto e^{\frac{-T}{T_0}}$ is established to the electrical conductivity of the Mott hopping model in one dimension. This removes the logical basis for arguing in favor of hopping conductivity in one dimension, $d=1\mathrm{}$, using the asymptotic form $\sigma \propto \exp [-{\left(\frac{T_0}{T}\right)}^{\frac{1}{\mathrm{}(1+d)\mathrm{}}}]$ as recently proposed for certain highly inhomogeneous solids.