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arXiv · hep-th/9710054

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

Mohamed Benarous
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Abstract

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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Mohamed Benarous. 1997-10-13. On the Poisson Structure of the Time-Dependent Mean-Field Equations for Systems of Bosons out of Equilibrium. https://doi.org/10.1006/aphy.1997.5755

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