Derivation of Hartree's theory for generic mean-field Bose systems
Derivation of Hartree's theory for generic mean-field Bose systems
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DOI：
10.1016/j.aim.2013.12.010
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发表时间：
2013-03
期刊：
影响因子：
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通讯作者：
Mathieu Lewin;P. T. Nam;N. Rougerie
中科院分区：
文献类型：
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作者：
Mathieu Lewin;P. T. Nam;N. Rougerie
在本文中，我们提供了一种新颖的策略来证明哈特里理论对于平均场体系中玻色量子系统基态能量的有效性。对于已知的俘获玻色气体的情况，这可以使用强量子 de Finetti 定理来证明，该定理给出了 k 粒子密度矩阵的无限层次结构。在这里，我们处理一些粒子被允许逃逸到无穷大，导致缺乏紧致性的情况。我们的方法基于两个要素：（1）量子德菲内蒂定理的弱版本，以及（2）多体系统的几何技术。我们的策略不依赖于粒子之间相互作用的任何特殊属性。特别是，我们的结果分别涵盖了玻色子原子和玻色子星的 Benguria-Lieb 和 Lieb-Yau 的结果。
In this paper we provide a novel strategy to prove the validity of Hartreeʼs 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 ofk-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.