MEAN-FIELD LIMIT OF BOSE-EINSTEIN CONDENSATES WITH ATTRACTIVE INTERACTIONS IN R2

doi:10.1016/S0252-9602(16)30001-7

数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (2): 317-324.doi: 10.1016/S0252-9602(16)30001-7

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MEAN-FIELD LIMIT OF BOSE-EINSTEIN CONDENSATES WITH ATTRACTIVE INTERACTIONS IN R²

郭玉劲¹, 陆璐²

1. Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China;
2. School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, China

收稿日期:2014-08-06 修回日期:2015-10-12 出版日期:2016-04-25 发布日期:2016-04-25
通讯作者: Lu Lu,E-mail:lulu@znufe.edu.cn E-mail:lulu@znufe.edu.cn
作者简介:Yujin Guo,E-mail:yjguo@wipm.ac.cn
基金资助:
This work is partially supported by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry of China, and National Center for Mathematics and Interdisciplinary Sciences in China.

MEAN-FIELD LIMIT OF BOSE-EINSTEIN CONDENSATES WITH ATTRACTIVE INTERACTIONS IN R²

Yujin GUO¹, Lu LU²

1. Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China;
2. School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, China

Received:2014-08-06 Revised:2015-10-12 Online:2016-04-25 Published:2016-04-25
Contact: Lu Lu,E-mail:lulu@znufe.edu.cn E-mail:lulu@znufe.edu.cn
Supported by:
This work is partially supported by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry of China, and National Center for Mathematics and Interdisciplinary Sciences in China.

摘要/Abstract

摘要：

Starting with the many-body Schrödinger Hamiltonian in R², we prove that the ground state energy of a two-dimensional interacting Bose gas with the pairwise attractive interaction approaches to the minimum of the Gross-Pitaevskii energy functional in the mean-field regime, as the particle number N→∞ and however the scattering length κ→0. By fixing N|κ|, this leads to the mean-field approximation of Bose-Einstein condensates with attractive interactions in R².

关键词: Bose-Einstein condensation, attractive interactions, Gross-Pitaevskii functional, mean-field approximation

Abstract:

Key words: Bose-Einstein condensation, attractive interactions, Gross-Pitaevskii functional, mean-field approximation

中图分类号:

35Q40

郭玉劲, 陆璐. MEAN-FIELD LIMIT OF BOSE-EINSTEIN CONDENSATES WITH ATTRACTIVE INTERACTIONS IN R²[J]. 数学物理学报(英文版), 2016, 36(2): 317-324.

Yujin GUO, Lu LU. MEAN-FIELD LIMIT OF BOSE-EINSTEIN CONDENSATES WITH ATTRACTIVE INTERACTIONS IN R²[J]. Acta mathematica scientia,Series B, 2016, 36(2): 317-324.

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MEAN-FIELD LIMIT OF BOSE-EINSTEIN CONDENSATES WITH ATTRACTIVE INTERACTIONS IN R²

MEAN-FIELD LIMIT OF BOSE-EINSTEIN CONDENSATES WITH ATTRACTIVE INTERACTIONS IN R²

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