Energy relaxation in the mean-field description of polariton condensates

We introduce a dissipation term in the Gross-Pitaevskii equation that describes the stimulated relaxation of condensed bosons due to scattering with different types of particles. This situation applies to Bose-Einstein condensates of quasi-particles in the solid state, such as magnons and excitons. Our model is compatible with the phenomenology of superfluidity: supercurrents are stable up to a critical speed and decay when they are faster. We apply our model to a description of the relaxation of polariton condensates in a shallow trap.