Random-matrix theory of mesoscopic fluctuations in conductors and superconductors

C. W. J. Beenakker

doi:10.1103/PhysRevB.47.15763

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Random-matrix theory of mesoscopic fluctuations in conductors and superconductors

C. W. J. Beenakker

DOI 10.1103/PhysRevB.47.15763 · Physical Review B

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Abstract

This paper contains a theoretical study of the sample-to-sample fluctuations in transport properties of phase-coherent, diffusive, quasi-one-dimensional systems. The main result is a formula for the variance of the fluctuations of an arbitrary linear statistic on the transmission eigenvalues [i.e., an observable of the form A=tsumn=1Nf(Tn)]. The formula is the analog of the Dyson-Mehta theorem in the statistical theory of energy levels. The analysis is based on an existing random-matrix theory for the joint probability distribution of the transmission eigenvalues Tn (n=1,2,...,N), and holds in the large-N limit. The variance of the fluctuations is shown to be independent of the sample size or degree of disorder and to have a universal 1/β dependence on the symmetry parameter β of the matrix ensemble. It follows that the universality which was established in the theory of ‘‘universal conductance fluctuations’’ is generic for a whole class of transport properties in mesoscopic conductors and superconductors. A further implication of the analysis is that the correlations between the transmission eigenvalues are not precisely described by a logarithmic interaction.