  The influence of a random field induced by impurities, boundary
irregularities etc. on the superfluidity of a quasi-two-dimensional (2D) system
of spatially indirect excitons in coupled quantum wells is studied. The
interaction between excitons is taken into account in the ladder approximation.
The random field is allowed to be large compared to the dipole-dipole repulsion
between excitons. The coherent potential approximation (CPA) allows us to
derive the exciton Green's function for a wide range of the random field, and
the CPA results are used in the weak-scattering limit, which results in the
second-order Born approximation. The Green's function of the collective
excitations for the cases of (1) equal electron and hole masses and (2) the
``heavy hole'' limit are derived analytically. 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. This puts
constraints on the experimental efforts to observe excitonic superfluidity.
