Dynamics of correlations in atomic Bose-Einstein condensates

The Gross-Pitaevskii equation has been extremely successful in the theory of weakly interacting Bose-Einstein condensates. However, present-day experiments reach beyond the regime of its validity due to the significant role of correlations. We review a method for tackling the dynamics of correlations in Bose condensed gases, in terms of non-commutative cumulants. This new approach has a wide applicability in the areas of current interest, e.g. the production of molecules and the manipulation of interactions in condensates. It also offers an interesting perspective on the classical-field methods for partly condensed Bose gases.