Universality of weak localization in disordered wires.

We compute the quantum correction δA due to weak localization for transport properties A = ∑ n a(Tn) of disordered quasi-one-dimensional conductors, by integrating the Dorokhov-Mello-Pereyra-Kumar equation for the distribution of the transmission eigenvalues Tn. The result δA = (1 − 2/β)[ 1 4 a(1) + ∫∞ 0 dx (4x + π2)−1a(cosh x)] is independent of sample length or mean free path, and has a universal 1 − 2/β dependence on the symmetry index β ∈ {1, 2, 4} of the ensemble of scattering matrices. This result generalizes the theory of weak localization for the conductance to all linear statistics on the transmission eigenvalues. PACS numbers: 73.50.Jt,72.10.Bg,72.15.Rn,74.80.Fp Typeset using REVTEX 1 Weak localization is a quantum transport effect which manifests itself as a magnetic-field dependent correction to the classical Drude conductance. Discovered in 1979, it was the first-known quantum interference effect on a transport property. (For reviews, see Ref. 3.) At zero temperature, and in the quasi-one-dimensional (quasi-1D) limit L ≫ W of a long and narrow wire (length L, width W ), the weak-localization correction to the conductance takes the universal form