Self-consistent quantum kinetics of condensate and non-condensate via a   coupled equation of motion formalism
  This paper extends an earlier quantum kinetics treatment for dilute, weakly-interacting, partially Bose-Einstein condensed gases, presented by the author elsewhere [J. Res. Natl. Inst. Stand. Technol. 101, 457 (1996)], by consistently treating the dynamics of the uncondensed atoms to the same level of approximation as the condensed atoms. Our method is based on a hierarchy of coupled equations of motion for the condensate mean field and fluctuations around this mean field, truncated to second order in the (effective two-body) interatomic potential, and with suitable decoupling approximations for higher order correlations. By applying perturbation theory in the Hartree-Fock-Bogoliubov basis, we re-derive the quantum kinetic theory of Walser et al. [Phys. Rev. A 59, 3878 (1999)], which further indicates the consistency of our treatment to the Kadanoff-Baym non-equilibrium Green's functions formalism for trapped gases. 
N. P. Proukakis