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期刊名称: Advances in Mathematics
Volume:254    Page:570-621
ISSN:0001-8708

Derivation of Hartreeʼs theory for generic mean-field Bose systems期刊论文

作者: Lewin Mathieu Nam Phan Thành Rougerie Nicolas
DOI:10.1016/j.aim.2013.12.010

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页码: 570-621
被引频次: 58
出版者: Elsevier Inc,ACADEMIC PRESS INC ELSEVIER SCIENCE,Elsevier
期刊名称: Advances in Mathematics
ISSN: 0001-8708
语言: English
摘要: 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 of -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.
相关主题: Many-particle Hamiltonian, Mean-field regime, Bosonic atoms, Hartree theory, Quantum de Finetti theorem, Boson stars, STATISTICAL-MECHANICS, GROUND-STATE, LIMIT, SCATTERING-THEORY, NORMAL STATES, BOSONS, MATHEMATICS, QUANTUM-MECHANICS, LARGE DEVIATION PRINCIPLE, CLASSICAL PARTICLES, GROSS-PITAEVSKII EQUATION, Mathematics, Spectral Theory, Mathematical Physics, Analysis of PDEs, Physics,

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