Unitarily inequivalent vacua in Bose-Einstein condensation of trapped gases

Masahiko Okumura*, Yoshiya Yamanaka

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


We approach the problem of the Bose-Einstein condensation of neutral atoms in an external trap, which is a finite system in size, from the viewpoint of quantum field theory. The phenomenon is considered as a spontaneous symmetry breakdown. The main result of this paper is that the vacua for this system with finite size and finite number of trapped neutral atoms, parametrized by different phases of the order parameter, are orthogonal to each other, namely the Fock spaces associated with each vacuum are unitarily inequivalent to each other. In the proof, the zero-energy mode which is the Nambu-Goldstone mode, and is discrete due to the presence of the trap, plays a crucial role. We introduce the discrete zero-energy mode in the formulation of the generalized Bogoliubov transformation and introduce an additional infinitesimal symmetry-breaking term in the Hamiltonian to control the zero-energy mode properly.

Original languageEnglish
Pages (from-to)429-445
Number of pages17
JournalPhysica A: Statistical Mechanics and its Applications
Issue number2
Publication statusPublished - 2006 Jun 15


  • Bose-Einstein condensation
  • Spontaneous symmetry breakdown
  • Unitarily inequivalent vacua

ASJC Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics


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