Recent developments in the scaling theory of phase-coherent conduction through a disordered wire are reviewed. 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.
Conductance distribution near the Anderson transition
