Disordered boson systems: A perturbative study

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Abstract
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 lifetime of the Bloch phonons in the regime of weak disorder. Generalizations of the present study to the strong disordered regime are discussed.
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