  We numerically study the dynamics of cold atoms in a two-dimensional
disordered potential. We consider an anisotropic speckle potential and focus on
the classical regime, which is relevant to some recent experiments. First, we
study the behavior of particles with a fixed energy and identify different
transport regimes. For low energy, the particles are classically localized due
to the absence of a percolating cluster. For high energy, the particles undergo
normal diffusion and we show that the diffusion constants scale algebraically
with the particle energy, with an anisotropy factor which significantly differs
from that of the disordered potential. For intermediate energy, we find a
transient sub-diffusive regime, which is relevant to the time scale of typical
experiments. Second, we study the behavior of a cold-atomic gas with an
arbitrary energy distribution, using the above results as a groundwork. We show
that the density profile of the atomic cloud in the diffusion regime is
strongly peaked and, in particular, that it is not Gaussian. Its behavior at
large distances allows us to extract the energy-dependent diffusion constants
from experimental density distributions. For a thermal cloud released into the
disordered potential, we show that our numerical predictions are in agreement
with experimental findings. Not only does this work give insights to recent
experimental results, but it may also serve interpretation of future
experiments searching for deviation from classical diffusion and traces of
Anderson localization.
