ON THE POISSON STRUCTURE OF THE TIME-DEPENDENT MEAN-FIELD EQUATIONS FOR SYSTEMS OF BOSONS OUT OF EQUILIBRIUM

We analyze the Poisson structure of the time-dependent meanfield equat ions for condensed bosons and construct the Lie-Poisson bracket associ ated to these equations. The latter follow from the time-dependent var iational principle of Balian and Veneroni when a Gaussian Ansatz is ch osen for the density operator. We perform a stability analysis of both the full and the linearized equations. We also search for canonically conjugate variables. In certain cases, the evolution equations can in deed be cast in a Hamiltonian form. (C) 1998 Academic Press.