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

• 论文 •    下一篇

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

郭玉劲1, 陆璐2   

  1. 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. 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:

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:

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.

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

中图分类号: 

  • 35Q40