Abstract
We analyze the Poisson structure of the time-dependent meanfield equations for condensed bosons and construct the Lie–Poisson bracket associated to these equations. The latter follow from the time-dependent variational principle of Balian and Vénéroni when a Gaussian Ansatz is chosen 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 indeed be cast in a Hamiltonian form.
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