  Anderson localization in a two-dimensional ultracold Bose-gas has been
demonstrated experimentally. Atoms were released within a dumbbell-shaped
optical trap, where the channel of variable aspect ratio provided the only path
for particles to travel between source and drain reservoirs. This channel can
be populated with columnar (repulsive) optical potential spikes of square cross
section with arbitrary pattern. These spikes constitute impurities, the
scattering centres for the otherwise free propagation of the particles. This
geometry does not allow for classical potential trapping which can be hard to
exclude in other experimental setups. Here we add further theoretical evidence
for Anderson localization in this system by comparing the transport processes
within a regular and a random pattern of impurities. It is demonstrated that
the transport within randomly distributed impurities is suppressed and the
corresponding localization length becomes shorter than the channel length.
However, if an equal density of impurities are distributed in a regular manner,
the transport is only modestly disturbed. This observation corroborates the
conclusions of the experimental observation: the localization is indeed
attributed to the disorder. Beyond analysing the density distribution and the
localization length, we also calculate a quantum `impedance' exhibiting
qualitatively different behaviour for regular and random impurity patterns.
