Conductance fluctuations in the localized regime

2006/03/29 by A. M. Somoza, Javier Prior, Somoza, A. M. +3 · 1 citation
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Quantum and electron transport phenomena #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.cond-mat/0603796

openalex publication_date 2006/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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