Variable range hopping in one-dimensional metals

Mott variable range hopping in one dimension is analyzed for a chain with a uniform distribution of localized states. We calculate the distribution of the largest hopping probabilities from states at the Fermi surface. The activated resistivity of Kurkij\"arvi is found to be an asymptotic limit valid for very long chains and low frequencies. An important anomalous hopping regime is found for intermediate lengths and times which crosses over into the quantum-mechanical regime. Experimental situations in anisotropic materials and for long wires and the relationship of the classical and quantum-mechanical frequency dependence are also discussed briefly.