  We study the onset of localization from excited states of trapped Bose-
Einstein Condensates expanding in presence of Gaussian uncorrelated random
disorder. In 1D systems, we observe that for a fixed ratio between the disorder
strength and the initial energy, excited states localize exponentially with a
localization length that decreases as the energy of the initial state
increases. Moreover, the localized state keeps the shape of the initial state
wave function with an exponential tail. In 2D, we analyze the interplay between
vorticiy and localization by examining the dispersion of a state containing a
vortex on it in a disordered media. Despite localization can be associated to
islands of constant phase, the presence of a vortex in the initial state leads
to dislocations and phase jumps in the localized state. The study of dispersion
of a bosonic condensate with vorticity bears similarities to the stability of
topological excitations in 2D p-wave fermionic superfluids.
