Derivation of Hartreeʼs theory for generic mean-field Bose systems |
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Authors: | Mathieu Lewin Phan Thành Nam Nicolas Rougerie |
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Institution: | 1. CNRS & Laboratoire de Mathématiques (UMR 8088), Université de Cergy-Pontoise, F-95000 Cergy-Pontoise, France;2. Université Grenoble 1 & CNRS, LPMMC (UMR 5493), B.P. 166, F-38 042 Grenoble, France |
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Abstract: | In this paper we provide a novel strategy to prove the validity of Hartree?s theory for the ground state energy of bosonic quantum systems in the mean-field regime. For the known case of trapped Bose gases, this can be shown using the strong quantum de Finetti theorem, which gives the structure of infinite hierarchies of k-particles density matrices. Here we deal with the case where some particles are allowed to escape to infinity, leading to a lack of compactness. Our approach is based on two ingredients: (1) a weak version of the quantum de Finetti theorem, and (2) geometric techniques for many-body systems. Our strategy does not rely on any special property of the interaction between the particles. In particular, our results cover those of Benguria–Lieb and Lieb–Yau for, respectively, bosonic atoms and boson stars. |
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Keywords: | 81V70 35Q40 |
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