  Bose-Einstein-condensed gases in external spatially random potentials are
considered in the frame of a stochastic self-consistent mean-field approach.
This method permits the treatment of the system properties for the whole range
of the interaction strength, from zero to infinity, as well as for arbitrarily
strong disorder. Besides a condensate and superfluid density, a glassy number
density due to a spatially inhomogeneous component of the condensate occurs.
For very weak interactions and sufficiently strong disorder, the superfluid
fraction can become smaller than the condensate fraction, while at relatively
strong interactions, the superfluid fraction is larger than the condensate
fraction for any strength of disorder. The condensate and superfluid fractions,
and the glassy fraction always coexist, being together either nonzero or zero.
In the presence of disorder, the condensate fraction becomes a nonmonotonic
function of the interaction strength, displaying an antidepletion effect caused
by the competition between the stabilizing role of the atomic interaction and
the destabilizing role of the disorder. With increasing disorder, the
condensate and superfluid fractions jump to zero at a critical value of the
disorder parameter by a first-order phase transition.
