  We study localization and charge dynamics in a monochromatically driven
one-dimensional Anderson insulator focussing on the low-frequency,
strong-driving regime. We study this problem using a mapping of the Floquet
Hamiltonian to a hopping problem with correlated disorder in one higher
harmonic-space dimension. We show that (i) resonances in this model correspond
to \emph{adiabatic} Landau-Zener (LZ) transitions that occur due to level
crossings between lattice sites over the course of dynamics; (ii) the
proliferation of these resonances leads to dynamics that \emph{appear}
diffusive over a single drive cycle, but the system always remains localized;
(iii) actual charge transport occurs over many drive cycles due to slow
dephasing between these LZ orbits and is logarithmic-in-time, with a crucial
role being played by far-off Mott-like resonances; and (iv) applying a
spatially-varying random phase to the drive tends to decrease localization,
suggestive of weak-localization physics. We derive the conditions for the
strong driving regime, determining the parametric dependencies of the size of
Floquet eigenstates, and time-scales associated with the dynamics, and
corroborate the findings using both numerical scaling collapses and analytical
arguments.
