Conductance and polarization in quantum junctions

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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.