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arXiv · 1409.1182

Th\'eor\`emes de de Finetti, limites de champ moyen et condensation de Bose-Einstein

Nicolas Rougerie
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Abstract

These lecture notes treat the mean-field approximation for equilibrium states of N body systems in classical and quantum statistical mechanics. A general strategy to justify effective models based on assumptions of statistical independence of the particles is in presented in detail. The main tools are a structure theorems of de Finetti that describe large N limits of states accessible to the systems in question, exploiting the indistinguishablity of particles. The focus is on quantum aspects, particularly the mean-field approximation for the ground state of a large system of bosons, in connection with Bose-Einstein condensation: structure of reduced density matrices of a large bosonic system, localization methods in Fock space, derivation of Hartree and non-linear Schr\"odinger effective energy functionals.

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Nicolas Rougerie. 2014-09-03. Th\'eor\`emes de de Finetti, limites de champ moyen et condensation de Bose-Einstein. https://arxiv.org/abs/1409.1182

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