中国物理B ›› 2006, Vol. 15 ›› Issue (7): 1577-1579.doi: 10.1088/1009-1963/15/7/033

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Spontaneous U(1) symmetry breaking and Bose--Einstein condensation

钱锋, 黄洪斌, 齐观晓, 沈才康   

  1. Department of Physics, Southeast University, Nanjing 210096, China
  • 收稿日期:2005-07-03 修回日期:2005-11-09 出版日期:2006-07-20 发布日期:2006-07-20
  • 基金资助:
    One of author (Huang H B) was partially supported by the Natural Science Foundation of Jiangsu province,China (Grant No BK2005062).

Spontaneous U(1) symmetry breaking and Bose--Einstein condensation

Qian Feng (钱锋), Huang Hong-Bin (黄洪斌), Qi Guan-Xiao (齐观晓), Shen Cai-Kang (沈才康)   

  1. Department of Physics, Southeast University, Nanjing 210096, China
  • Received:2005-07-03 Revised:2005-11-09 Online:2006-07-20 Published:2006-07-20
  • Supported by:
    One of author (Huang H B) was partially supported by the Natural Science Foundation of Jiangsu province,China (Grant No BK2005062).

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摘要： Based on Bogoliubov's truncated Hamiltonian HB for a weakly interacting Bose system, and adding a U(1) symmetry breaking term $\sqrt{V}(\lambda a0+\lambda*a0+) to HB, we show by using the coherent state theory and the mean-field approximation rather than the c-number approximations, that the Bose--Einstein condensation(BEC) occurs if and only if the U(1) symmetry of the system is spontaneously broken. The real ground state energy and the justification of the Bogoliubov c-number substitution are given by solving the Schr\"{o}dinger eigenvalue equation and using the self-consistent condition.

关键词: BEC, U(1) symmetry breaking, generalized SU(1, 1), coherent state

Abstract: Based on Bogoliubov's truncated Hamiltonian HB for a weakly interacting Bose system, and adding a U(1) symmetry breaking term $\sqrt{V}(\lambda a_0+\lambda^* a_0^+)$ to HB, we show by using the coherent state theory and the mean-field approximation rather than the c-number approximations, that the Bose--Einstein condensation(BEC) occurs if and only if the U(1) symmetry of the system is spontaneously broken. The real ground state energy and the justification of the Bogoliubov c-number substitution are given by solving the Schr\"{o}dinger eigenvalue equation and using the self-consistent condition.

Key words: BEC, U(1) symmetry breaking, generalized SU(1, 1), coherent state

中图分类号:  (Other Bose-Einstein condensation phenomena)

  • 03.75.Nt
03.65.Ge (Solutions of wave equations: bound states)