Derivation of Hartree's theory for generic mean-field Bose systems

By Mathieu Lewin, Phan Thanh Nam, Nicolas Rougerie. 2013

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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 well-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.

View Paper: https://www.semanticscholar.org/paper/d3f0127f2db6cd29f7c22a5ea65516ffae4c691b

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Citations in the corpus

Bogoliubov Spectrum of Interacting Bose Gases (2012, background): “This is discussed in the recent work [32], based on a compactness argument which does not provide any explicit error estimate.”