UNIVERSALITY OF WEAK-LOCALIZATION IN DISORDERED WIRES

We compute the quantum correction delta A due to weak localization for transport properties A = Sigma(n)a(T-n) of disordered quasi-one-dimensional conductors, by integrating the Dorokhov-Mello-Pereyra-Kumar equation for the distribution of the transmission eigenvalues T-n. The result delta A = (1 - 2/beta) [1/4 a(1) + integral(0)(infinity) dx (4x(2) pi(2))(-1) a(cosh(-2) x)] is independent of sample length or mean free path, and has a universal 1 - 2/beta dependence on the symmetry index beta epsilon {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.