  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.

Quantum Gases;Disordered Systems and Neural Networks;Quantum Physics