The Landauer formula expresses the conductance of a disordered one-dimensional conductor as the ratio of transmission ($T$) to reflection ($R$) coefficients of scattered waves, $G=\left(\frac{e^2}{2\pi \hslash }\right)\left(\frac{T}{R}\right)$. We give a rigorous derivation of this formula from linear-response theory (Kubo formula). The generalization to the many-scattering-channel case is given in detail. It is found that only in very special circumstances can the currents in different channels be decoupled in such a way as to give a simple conductance formula.

• Received 23 March 1981

DOI:https://doi.org/10.1103/PhysRevB.24.2978