Exact results for the level density and two-point correlation function of the transmission-matrix eigenvalues in quasi-one-dimensional conductors

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Abstract
We study transport properties of phase-coherent quasi-one-dimensional disordered conductors in the diffusive regime, in terms of the eigenvalue distribution of the two-terminal transmission matrix. Using an expansion in inverse powers of the classical conductance, we calculate the average transmission eigenvalue density and the two-point correlation function for fluctuations in the density. A formula for the average value and the variance of a general linear statistic on the transmission eigenvalues is obtained. Our results confirm an earlier hypothesis, based on random-matrix theory, that fluctuations are universal in the diffusive regime and ultimately determined by level repulsion.