Dynamical instability induced by the zero mode under symmetry breaking external perturbation

    Research output: Contribution to journalArticle

    2 Citations (Scopus)

    Abstract

    A complex eigenvalue in the Bogoliubov-de Gennes equations for a stationary Bose-Einstein condensate in the ultracold atomic system indicates the dynamical instability of the system. We also have the modes with zero eigenvalues for the condensate, called the zero modes, which originate from the spontaneous breakdown of symmetries. Although the zero modes are suppressed in many theoretical analyses, we take account of them in this paper and argue that a zero mode can change into one with a pure imaginary eigenvalue by applying a symmetry breaking external perturbation potential. This emergence of a pure imaginary mode adds a new type of scenario of dynamical instability to that characterized by the complex eigenvalue of the usual excitation modes. For illustration, we deal with two one-dimensional homogeneous Bose-Einstein condensate systems with a single dark soliton under a respective perturbation potential, breaking the invariance under translation, to derive pure imaginary modes.

    Original languageEnglish
    Pages (from-to)250-260
    Number of pages11
    JournalAnnals of Physics
    Volume347
    DOIs
    Publication statusPublished - 2014

    Fingerprint

    broken symmetry
    perturbation
    eigenvalues
    Bose-Einstein condensates
    condensates
    invariance
    solitary waves
    breakdown
    symmetry
    excitation

    Keywords

    • Bose-Einstein condensation
    • Dark soliton
    • Dynamical instability
    • Zero mode

    ASJC Scopus subject areas

    • Physics and Astronomy(all)

    Cite this

    Dynamical instability induced by the zero mode under symmetry breaking external perturbation. / Takahashi, Junichi; Nakamura, Y.; Yamanaka, Yoshiya.

    In: Annals of Physics, Vol. 347, 2014, p. 250-260.

    Research output: Contribution to journalArticle

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