Excitations in a non-equilibrium Bose-Einstein condensate of exciton-polaritons

We have developed a mean-field model to describe the dynamics of a non-equilibrium Bose-Einstein condensate of exciton-polaritons in a semiconductor microcavity. The spectrum of elementary excitations around the stationary state is analytically studied in different geometries. A diffusive behaviour of the Goldstone mode is found in the spatially homogeneous case and new features are predicted for the Josephson effect in a two-well geometry.