Unitarily inequivalent vacua in Bose-Einstein condensation of trapped gases

Masahiko Okumura, Yoshiya Yamanaka

    Research output: Contribution to journalArticle

    2 Citations (Scopus)

    Abstract

    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
    Volume365
    Issue number2
    DOIs
    Publication statusPublished - 2006 Jun 15

    Fingerprint

    Bose-Einstein Condensation
    condensation
    Trap
    Zero
    neutral atoms
    Energy
    gases
    Fock Space
    traps
    Quantum Field Theory
    Symmetry Breaking
    Order Parameter
    Breakdown
    Vacuum
    energy
    Symmetry
    broken symmetry
    Formulation
    breakdown
    Term

    Keywords

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

    ASJC Scopus subject areas

    • Mathematical Physics
    • Statistical and Nonlinear Physics

    Cite this

    Unitarily inequivalent vacua in Bose-Einstein condensation of trapped gases. / Okumura, Masahiko; Yamanaka, Yoshiya.

    In: Physica A: Statistical Mechanics and its Applications, Vol. 365, No. 2, 15.06.2006, p. 429-445.

    Research output: Contribution to journalArticle

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