  Spectral excitations of ultracold gases of bosonic atoms trapped in one
dimensional optical lattices with disorder are investigated by means of the
variational cluster approach applied to the Bose-Hubbard model. In particular,
qualitatively different disorder distributions typically employed in
experiments are considered. The computed spectra exhibit a strong dependence on
both the shape of the disorder distribution and the disorder strength. We
compare alternative results for the Mott gap obtained from its formal
definition and from the minimum peak distance, which is the quantity available
from experiments.
