Differentiable potentials and metallic states in disordered one-dimensional systems

We provide evidence that as a general rule Anderson localization effects become weaker as the degree of differentiability of the disordered potential increases. In one dimension a band of metallic states exists provided that the disordered potential is sufficiently correlated and has some minimum degree of differentiability. Several examples are studied in detail. In agreement with the one parameter scaling theory the motion in the metallic region is ballistic if the spectral density is smooth. Finally, we study the most promising settings to observe these results in the context of cold atoms.