# 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…

## 52 Citations

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