A new expression for the conductance of quantum junctions within interacting {\it ab-initio} approaches

We present a new expression for the conductance of a quantum junction~[1] that is both physically appealing and numerically adventageous. First, it shows that conductance represents a strength of the Drude singularity of the conductivity $\sigma(k,k';i\omega)$ and properly accounts for the experimental bias that results from the total field. The numerical advantage comes from the fact that instead of the current-current correlation function it is expressed in terms of density-density response which is far easier to evaluate. If formulated within time-dependent density-functional theory, it explicitly uses the exchange-correlation kernel $f_{xc}$ or, when used within many-body perturbation theory, it makes use of the irreducible polarisation function $P(k,k';i\omega)$. We will present its numerical implementation for a model metal-vacuum-metal interface. \\ \noindent [1] P. Bokes and R. W. Godby, Phys. Rev. B 69, 245420 (2004).