Acta mathematica scientia,Series B ›› 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

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.

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

CLC Number: 

  • 35Q40
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