  We have studied theoretically the Bose-Einstein condensation (BEC) of
two-dimensional excitons in a ring with small random width variation. We derive
a nonlinear Gross-Pitaevkii equation (GPE) for such a condensate. Our numerical
solution of the ground state of the GPE displays a necklace-like structure in
the presence of small random variation of ring width. This is a consequence of
the interplay between random potential and the nonlinear repulsive term of the
GPE. Our result suggests that the formation of ring and necklace-like
structures observed recently in the photoluminescence of quantum wells may be
stable even in the BEC phase.
