  Recent advances in transport properties measurements of disordered materials
and lattice simulations, using superconducting qubits, have rekindled interest
in Anderson localization, motivating our study of highly disordered quantum
lattices. Initially, our statistical analysis of localized eigenstates reveals
a distinct transition between weak and strong disorder regimes, suggesting a
random distribution of dimers in highly disordered systems. Subsequently, the
random dimer model predicts an oscillating diffusivity that decays as
$t^{-1/2}$, is inversely proportional to the disorder strength, and maintains a
constant frequency with an initial phase shift of $\pi/4$. The first peak
exhibits a universal scaling of $\sigma^{-1}$ both in peak time and amplitude.
Finally, we find that stochastic noise suppresses these oscillations and
induces hopping between localized eigenstates, resulting in constant diffusion
over long times. Our predictions challenge the conventional understanding of
incoherent hopping under strong disorder. This offers new insights to optimize
disordered systems for optoelectrical and quantum information technologies.
