  We investigate the properties of the superfluid phase in the
three-dimensional disordered Bose-Hubbard model using Quantum Monte-Carlo
simulations. The phase diagram is generated using Gaussian disorder on the
on-site potential. Comparisons with box and speckle disorder show qualitative
similarities leading to the re-entrant behavior of the superfluid. Quantitative
differences that arise are controlled by the specific shape of the disorder.
Statistics pertaining to disorder distributions are studied for a range of
interaction strengths and system sizes, where strong finite-size effects are
observed. Despite this, both the superfluid fraction and compressibility remain
self-averaging throughout the superfluid phase. Close to the
superfluid-Bose-glass phase boundary, finite-size effects dominate but still
suggest that self-averaging holds. Our results are pertinent to experiments
with ultracold atomic gases where a systematic disorder averaging procedure is
typically not possible.
