  We study the high temperature transport behavior of the Aubry-Andr\'e-Harper
(AAH) model, both in the isolated thermodynamic limit and in the open system.
At the critical point of the AAH model, we find hints of super-diffusive
behavior from the scaling of spread of an initially localized wavepacket. On
the other hand, when connected to two baths with different chemical potentials
at the two ends, we find that the critical point shows clear sub-diffusive
scaling of current with system size. We provide an explanation of this by
showing that the current scaling with system-size is entirely governed by the
behavior of the single particle eigenfunctions at the boundary sites where
baths are attached. We also look at the particle density profile in
non-equilibrium steady state of the open system when the two baths are at
different chemical potentials. We find that the particle density profile has
distinctly different behavior in the delocalized, critical and localized phases
of the AAH model.
