Derivation of nonlinear Gibbs measures from many-body quantum mechanics

@article{Lewin2014DerivationON,
  title={Derivation of nonlinear Gibbs measures from many-body quantum mechanics},
  author={Mathieu Lewin and Phan Th{\`a}nh Nam and Nicolas Rougerie},
  journal={arXiv: Mathematical Physics},
  year={2014}
}
We prove that nonlinear Gibbs measures can be obtained from the corresponding many-body, grand-canonical, quantum Gibbs states, in a mean-field limit where the temperature T diverges and the interaction behaves as 1/T. We proceed by characterizing the interacting Gibbs state as minimizing a functional counting the free-energy relatively to the non-interacting case. We then perform an infinite-dimensional analogue of phase-space semiclassical analysis, using fine properties of the quantum… 
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