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Exactly Solvable Scaling Theory of Conduction in Disordered Wires

C. W. J. Beenakker
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Abstract

Recent developments are reviewed in the scaling theory of phase-coherent conduction through a disordered wire. The Dorokhov-Mello-Pereyra-Kumar equation for the distribution of transmission eigenvalues has been solved exactly, in the absence of time-reversal symmetry. Comparison with the previous prediction of random-matrix theory shows that this prediction was highly accurate --- but not exact: The repulsion of the smallest eigenvalues was overestimated by a factor of two. This factor of two resolves several disturbing discrepancies between random-matrix theory and microscopic calculations, notably in the magnitude of the universal conductance fluctuations in the metallic regime, and in the width of the log-normal conductance distribution in the insulating regime. ***To be published as a "Brief Review" in Modern Physics Letters B.****

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C. W. J. Beenakker. 1994-03-09. Exactly Solvable Scaling Theory of Conduction in Disordered Wires. https://doi.org/10.1142/s0217984994000509

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