Reversible and irreversible evolution of a condensed bosonic gas

We have formulated a kinetic theory for a condensed atomic gas in a trap, i.e., a generalized Gross-Pitaevskii equation, as well as a quantum-Boltzmann equation for the normal and anomalous fluctuations [R. Walser et al., Phys. Rev. A 59, 3878 (1999)]. In this paper, the theory is applied to the case of an isotropic configuration and we present numerical and analytical results for the reversible real-time propagation, as well as irreversible evolution towards equilibrium.