  We study charge transport in the Peierls-Harper model with a quasi-periodic
cosine potential. We compute the Landauer-type conductance of the wire. Our
numerical results show the following: (i) When the Fermi energy lies in the
absolutely continuous spectrum that is realized in the regime of the weak
coupling, the conductance is quantized to the universal conductance. (ii) For
the regime of localization that is realized for the strong coupling, the
conductance is always vanishing irrespective of the value of the Fermi energy.
Unfortunately, we cannot make a definite conclusion about the case with the
critical coupling. We also compute the conductance of the Thue-Morse model.
Although the potential of the model is not quasi-periodic, the energy spectrum
is known to be a Cantor set with zero Lebesgue measure. Our numerical results
for the Thue-Morse model also show the quantization of the conductance at many
locations of the Fermi energy, except for the trivial localization regime.
Besides, for the rest of the values of the Fermi energy, the conductance shows
a similar behavior to that of the Peierls-Harper model with the critical
coupling.
