Collective-variables description of the atomic-recoil laser

We propose a description of the collective atomic-recoil laser based on a set of nonlinear differential equations for an appropriate set of collective variables. The main obvious advantage of this description is that, when applicable, it can describe systems having an arbitrary number of particles. A comparison between the predictions of the collective equations and those of their microscopic counterparts shows a satisfactory level of accuracy, even during the nonlinear stage of the evolution. The linearized version of the collective equations is especially useful for the study of the small-signal gain or absorption spectrum and the analysis of the start-up process.