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Conductance fluctuations in the localized regime

A. M. Somoza·J. Prior·M. Ortuno
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Abstract

We have studied numerically the fluctuations of the conductance, $g$, in two-dimensional, three-dimensional and four-dimensional disordered non-interacting systems. We have checked that the variance of $\ln g$ varies with the lateral sample size as $L^{2/5}$ in three-dimensional systems, and as a logarithm in four-dimensional systems. The precise knowledge of the dependence of this variance with system size allows us to test the single-parameter scaling hypothesis in three-dimensional systems. We have also calculated the third cumulant of the distribution of $\ln g$ in two- and three-dimensional systems, and have found that in both cases it diverges with the exponent of the variance times 3/2, remaining relevant in the large size limit.

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A. M. Somoza, J. Prior, M. Ortuno. 2006-03-29. Conductance fluctuations in the localized regime. https://arxiv.org/abs/cond-mat/0603796

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