  We characterize the absolutely continuous spectrum of the one-dimensional
Schr\"odinger operators $h=-\Delta+v$ acting on $\ell^2(\mathbb{Z}_+)$ in terms
of the limiting behavior of the Landauer-B\"uttiker and Thouless conductances
of the associated finite samples. The finite sample is defined by restricting
$h$ to a finite interval $[1,L]\cap\mathbb{Z}_+$ and the conductance refers to
the charge current across the sample in the open quantum system obtained by
attaching independent electronic reservoirs to the sample ends. Our main result
is that the conductances associated to an energy interval $I$ are non-vanishing
in the limit $L\to\infty$ iff ${\rm sp}_{\rm ac}(h)\cap I=\emptyset$. We also
discuss the relationship between this result and the Schr\"odinger Conjecture.
