Phase diagram of the 3D Anderson model for uncorrelated speckle potentials

TL;DR

This paper maps the phase diagram of 3D Anderson localization in uncorrelated speckle potentials, revealing asymmetries in mobility edges consistent with recent numerical findings.

Contribution

It provides a theoretical analysis of localization in speckle potentials using the CPA and transfer-matrix methods, explaining the asymmetry in mobility edges.

Findings

Good agreement between CPA and exact numerics for Green's function

Phase diagram shape explained by self-consistent localization theory

Asymmetry in mobility edges for blue and red speckles confirmed

Abstract

We investigate the localization properties of atoms moving in a three-dimensional optical lattice in the presence of an uncorrelated disorder potential having the same probability distribution $P(V)$ as laser speckles. We find that the disorder-averaged (single-particle) Green's function, calculated via the coherent potential approximation, is in very good agreement with exact numerics. Using the transfer-matrix method, we compute the phase diagram in the energy-disorder plane and show that its peculiar shape can be understood from the self-consistent theory of localization. In particular, we recover the large asymmetry in the position of the mobility edge for blue and red speckles, which was recently observed numerically for correlated speckle potentials.