A hard-core disordered boson system is mapped onto a quantum spin 1/2
XY-model with transverse random fields. It is then generalized to a system of
spins with an arbitrary magnitude S and studied through a 1/S expansion. The
first order 1/S expansion corresponds to a spin-wave theory. The effect of weak
disorder is studied perturbatively within such a first order 1/S scheme. We
compute the reduction of the speed of sound and the life time of the Bloch
phonons in the regime of weak disorder. Generalizations of the present study to
the strong disordered regime are discussed.Comment: 27 pages, revte