Relation between conductivity and transmission matrix

Abstract

The dc conductance $\Gamma$ of a finite system with static disorder is related to its transmission matrix $t$ by the simple relation $\Gamma =\left(\frac{e^2}{2\pi \hslash }\right) \mathrm{Tr}\left(t^{†}t\right)$. This relation is derived from the Kubo formula and is valid for any number of scattering channels with or without time-reversal symmetry. Differences between various definitions of the conductance of a finite system are discussed.