Calculation of the temperature-dependent mobility transition for small-polaron hopping in one dimension

Exact expressions for the dc mobility of a small polaron hopping on a one-dimensional disordered lattice are derived. Several features are observed: (i) linear response is recovered in the limit of vanishing applied fields, in spite of the presence of random biases, (ii) the nondecaying part of the polaron memory function does not contribute to the dc mobility for a diagonally disordered system, and (iii) for a Gaussian distribution of site energies, the mobility vanishes below a transition temperature T0. It is shown that at a temperature T near the transition point, the mobility scales as μ∼(T-T0)1/2.