  The theory of what happens to a superfluid in a random field, known as the
``dirty boson'' problem, directly relates to a real experimental system
presently under study by several groups, namely excitons in coupled
semiconductor quantum wells. We consider the case of bosons in two dimensions
in a random field, when the random field can be large compared to the repulsive
exciton-exciton interaction energy, but is small compared to the exciton
binding energy. The interaction between excitons is taken into account in the
ladder approximation. The coherent potential approximation allows us to derive
the exciton Green's function for a wide range of the random field strength, and
in the weak-scattering limit CPA results in the second-order Born
approximation. For quasi-two-dimensional excitonic systems, the density of the
superfluid component and the Kosterlitz-Thouless temperature of the superfluid
phase transition are obtained, and are found to decrease as the random field
increases.
