Conductance and polarization in quantum junctions

We revisit the expression for the conductance of a general nanostructure---such as a quantum point contact---as obtained from the linear-response theory. We show that the conductance represents the strength of the Drude singularity in the conductivity σ(k,k^';iω→0). Using the equation of continuity for electric charge we obtain a formula for conductance in terms of polarization of the system. This identification can be used for direct calculation of the conductance for systems of interest even at the ab initio level. In particular, we show that one can evaluate the conductance from calculations for a finite system without the need for special ``transport'' boundary conditions.