Universality of weak localization in disordered wires

We compute the quantum correction δA due to weak localization for transport properties A= ${\mathit{tsum}}_{\mathit{n}}$ a(${\mathit{T}}_{\mathit{n}}$) of disordered quasi-one-dimensional conductors, by integrating the Dorokhov-Mello-Pererya-Kumar equation for the distribution of the transmission eigenvalues ${\mathit{T}}_{\mathit{n}}$. The result δA=(1-2/β)[1/4a(1)+${\mathcal{F}}_0^{\mathrm{\infty }}$dx(4${\mathit{x}}^2$+${\mathrm{\pi }}^2$ ${)}^{\mathrm{-}1}$a(${\cosh }^{\mathrm{-}2}$ 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.