TY - JOUR
AB - 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 strength 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 relative entropy, the link between quantum de Finetti measures and upper/lower symbols in a coherent state basis, as well as Berezin-Lieb type inequalities. Our results cover the measure built on the defocusing nonlinear SchrÃ¶dinger functional on a finite interval, as well as smoother interactions in dimensions d 2.
AU - Lewin, Mathieu
AU - Phan Thanh, Nam
AU - Rougerie, Nicolas
ID - 473
JF - Journal de l'Ecole Polytechnique - Mathematiques
TI - Derivation of nonlinear gibbs measures from many-body quantum mechanics
VL - 2
ER -