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We study the superfluid transitions in bidimensional (2D) and tridimensional(3D) disordered and interacting Bose gases. We work in the limit of long-rangecorrelated disorder such that it can be treated in the local densityapproximation. We present the superfluid transition curves both in thedisorder-temperature plane well as in the disorder-entropy plane in 2D and 3DBose gases. Surprisingly, we find that a small amount of disorder is alwaysfavorable to the apparition of a superfluid. Our results offer a quantitativecomparison with recent experiments in 2D disordered ultra-cold gases, for whichno exact theory exists.

Phase diagrams of 2D and 3D disordered Bose gases in the local density approximation