Interacting multiple zero mode formulation and its application to a system consisting of a dark soliton in a condensate

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    Abstract

    To formulate the zero modes in a finite-size system with spontaneous breakdown of symmetries in quantum field theory is not trivial, for in the naive Bogoliubov theory, one encounters difficulties such as phase diffusion, the absence of a definite criterion for determining the ground state, and infrared divergences. An interacting zero mode formulation that has been proposed for systems with a single zero mode to avoid these difficulties is extended to general systems with multiple zero modes. It naturally and definitely gives the interactions among the quantized zero modes, the consequences of which can be observed experimentally. In this paper, as a typical example, we consider an atomic Bose-Einstein condensed system with a dark soliton that contains two zero modes corresponding to the spontaneous breakdown of the U(1) gauge and translational symmetries. Then we evaluate the standard deviations of the zero mode operators and see how the mutual interaction between the two zero modes affects them.

    Original languageEnglish
    Article number023627
    JournalPhysical Review A - Atomic, Molecular, and Optical Physics
    Volume92
    Issue number2
    DOIs
    Publication statusPublished - 2015 Aug 18

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    condensates
    solitary waves
    formulations
    breakdown
    Bogoliubov theory
    symmetry
    encounters
    standard deviation
    divergence
    interactions
    operators
    ground state

    ASJC Scopus subject areas

    • Atomic and Molecular Physics, and Optics

    Cite this

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    title = "Interacting multiple zero mode formulation and its application to a system consisting of a dark soliton in a condensate",
    abstract = "To formulate the zero modes in a finite-size system with spontaneous breakdown of symmetries in quantum field theory is not trivial, for in the naive Bogoliubov theory, one encounters difficulties such as phase diffusion, the absence of a definite criterion for determining the ground state, and infrared divergences. An interacting zero mode formulation that has been proposed for systems with a single zero mode to avoid these difficulties is extended to general systems with multiple zero modes. It naturally and definitely gives the interactions among the quantized zero modes, the consequences of which can be observed experimentally. In this paper, as a typical example, we consider an atomic Bose-Einstein condensed system with a dark soliton that contains two zero modes corresponding to the spontaneous breakdown of the U(1) gauge and translational symmetries. Then we evaluate the standard deviations of the zero mode operators and see how the mutual interaction between the two zero modes affects them.",
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    AU - Nakamura, Y.

    AU - Yamanaka, Yoshiya

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