Goldstone theorem, Hugenholtz-Pines theorem, and Ward-Takahashi relation in finite volume Bose-Einstein condensed gases

Hiroaki Enomoto, Masahiko Okumura, Yoshiya Yamanaka

    Research output: Contribution to journalArticle

    6 Citations (Scopus)

    Abstract

    We construct an approximate scheme based on the concept of the spontaneous symmetry breakdown, satisfying the Goldstone theorem, for finite volume Bose-Einstein condensed gases in both zero and finite temperature cases. In this paper, we discuss the Bose-Einstein condensation in a box with periodic boundary condition and do not assume the thermodynamic limit. When energy spectrum is discrete, we found that it is necessary to deal with the Nambu-Goldstone mode explicitly without the Bogoliubov's prescription, in which zero-mode creation- and annihilation-operators are replaced with a c-number by hand, for satisfying the Goldstone theorem. Furthermore, we confirm that the unitarily inequivalence of vacua in the spontaneous symmetry breakdown is true for the finite volume system.

    Original languageEnglish
    Pages (from-to)1892-1917
    Number of pages26
    JournalAnnals of Physics
    Volume321
    Issue number8
    DOIs
    Publication statusPublished - 2006 Aug

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    theorems
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    energy spectra
    condensation
    boundary conditions
    operators
    thermodynamics
    temperature

    Keywords

    • Bose-Einstein condensation
    • Goldstone theorem
    • Hugenholtz-Pines theorem
    • Spontaneous symmetry breakdown
    • Unitarily inequivalent vacua
    • Ward-Takahashi relations

    ASJC Scopus subject areas

    • Physics and Astronomy(all)

    Cite this

    Goldstone theorem, Hugenholtz-Pines theorem, and Ward-Takahashi relation in finite volume Bose-Einstein condensed gases. / Enomoto, Hiroaki; Okumura, Masahiko; Yamanaka, Yoshiya.

    In: Annals of Physics, Vol. 321, No. 8, 08.2006, p. 1892-1917.

    Research output: Contribution to journalArticle

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