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We study the problem of disordered interacting bosons within grand-canonicalthermodynamics and Bogoliubov theory. We compute the fractions of condensed andnon-condensed particles and corrections to the compressibility and the speed ofsound due to interaction and disorder. There are two small parameters, thedisorder strength compared to the chemical potential and the dilute-gasparameter.

A grand-canonical approach to the disordered Bose gas