  There has been a revival of interest in localization phenomena in
quasiperiodic systems with a view to examining how they differ fundamentally
from such phenomena in random systems. Mo- tivated by this, we study transport
in the quasiperiodic, one-dimentional (1d) Aubry-Andre model and its
generalizations to 2d and 3d. We study the conductance of open systems,
connected to leads, as well as the Thouless conductance, which measures the
response of a closed system to boundary perturbations. We find that these
conductances show signatures of a metal-insulator transition from an insulator,
with localized states, to a metal, with extended states having (a) ballistic
transport (1d), (b) superdiffusive transport (2d), or (c) diffusive transport
(3d); precisely at the transition, the system displays sub-diffusive critical
states. We calculate the beta function $\beta(g) = dln(g)/dln(L)$ and show
that, in 1d and 2d, single-parameter scaling is unable to describe the
transition. Further- more, the conductances show strong non-monotonic
variations with L and an intricate structure of resonant peaks and subpeaks. In
1d the positions of these peaks can be related precisely to the prop- erties of
the number that characterizes the quasiperiodicity of the potential; and the
L-dependence of the Thouless conductance is multifractal. We find that, as d
increases, this non-monotonic de- pendence of g on L decreases and, in 3d, our
results for $\beta(g)$ are reasonably well approximated by single-parameter
scaling.
