Quantum fluctuations of the conductance in the hopping regime

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Abstract
The results of the numerical scaling approach for localization are used to discuss the statistical behaviour of the zero-temperature conductance of disordered systems of finite size. In the asymptotic regime of strong localization, where transport is dominated by hopping processes, explicit expressions for the temperature dependence of the fluctuations of the conductance and the resistance are obtained by assuming that the phase coherence length is given by the Mott hopping law. It is shown that the temperature dependence of the fluctuations of the logarithm of the conductance/resistance does not depend on the assumptions concerning the statistics of the hopping processes. The results are compared with other theoretical and experimental approaches.