Abstract
We study quantum effects on Mott's variable-range hopping in one-dimensional (1D) and two-dimensional (2D) systems. In most experimental situations, wave functions are not extremely localized and fluctuations in the localization length are important. We argue that, in order to compare with experiments, it is necessary to consider an effective localization length for hopping different than the standard one, deduced from the zero-temperature conductance. Also, although quantum fluctuations do not qualitatively change Mott's law, they increase the average resistance in 1D systems. They do not alter much the results in 2D systems.