Differentiable potentials and metallic states in disordered one-dimensional systems

TL;DR

This paper shows that increasing the differentiability of disordered potentials in one-dimensional systems weakens Anderson localization, allowing for metallic states under certain correlated and smooth potential conditions, with implications for cold atom experiments.

Contribution

It demonstrates that higher differentiability of disordered potentials can induce metallic states in 1D systems, expanding understanding of localization phenomena.

Findings

Metallic states exist in 1D disordered systems with sufficiently correlated and differentiable potentials.

Ballistic motion occurs in the metallic region when the spectral density is smooth.

Potential experimental observation in cold atom setups is discussed.

Abstract

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.