  Introducing disorder into the Bose-Hubbard model at integer fillings leads to
a Bose glass phase, along with the Mott insulator and superfluid phases. We
suggest a new order parameter: the determinant of the one body density matrix,
which is nonzero only within the Mott-insulator phase. Alongside the superfluid
fraction, it is then possible to distinguish the three phases. The Bose glass
phase is the only phase which has vanishing determinant and superfluid
fraction. The vanishing of the determinant in the Bose glass phase occurs due
to the partial fragmentation of the condensate into localized fragments, each
with zero superfluid response, which implies the presence of unoccupied sites
and hence the presence of lines of zeros in the one body density matrix. In the
superfluid phase, the determinant vanish for another reason - due to the
macroscopic occupation of a single particle state. Finally, we suggest the
enhancement of the three body decay rate in the Bose glass phase, as an
experimental indicator for the presence of localized fragments.
