On the Poisson Structure of the Time-Dependent Mean-Field Equations for Systems of Bosons out of Equilibrium

Details On the Poisson Structure of the Time-Dependent Mean-Field Equations for Systems of Bosons out of Equilibrium On the Poisson Structure of the Time-Dependent Mean-Field Equations for Systems of Bosons out of Equilibrium

1997-10-07

arxiv.org/abs/hep-th/9710054v2

Annals Phys. 264 (1998) 1-12

Physics

High Energy Physics

High Energy Physics - Theory

21 pages. To appear in Annals of Physics

Scientific paper

10.1006/aphy.1997.5755

We analyze the Poisson structure of the time-dependent mean-field equations for bosons and construct the Lie-Poisson bracket associated to these equations. The latter follow from the time-dependent variational principle of Balian and Veneroni 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 the canonically conjugate variables. In certain cases, the evolution equations can indeed be cast in a Hamiltonian form.

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