Random-matrix theory of mesoscopic fluctuations in conductors and superconductors

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=${\mathit{tsum}}_{\mathit{n}=1\mathrm{}}^{\mathit{N}}$f(${\mathit{T}}_{\mathit{n}}$)]. 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 ${\mathit{T}}_{\mathit{n}}$ (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.