Random potential and modulation of the order parameter of exciton bose-einstein condensate in a ring

We have studied theoretically the Bose-Einstein condensation (BEC) of two-dimensional excitons in a ring with a small random variation of the effective exciton potential along the circumference. We derive a nonlinear Gross-Pitaevskii equation (GPE) for such a condensate, which is valid even in the presence of a weak magnetic field. For several types of random potentials, our numerical solution of the ground state of the GPE displays a necklace-like structure. This is a consequence of the interplay between the random potential and a strong nonlinear repulsive term in the GPE.