### 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 language | English |
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Article number | 023627 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 92 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2015 Aug 18 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

**Interacting multiple zero mode formulation and its application to a system consisting of a dark soliton in a condensate.** / Takahashi, Junichi; Nakamura, Y.; Yamanaka, Yoshiya.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Interacting multiple zero mode formulation and its application to a system consisting of a dark soliton in a condensate

AU - Takahashi, Junichi

AU - Nakamura, Y.

AU - Yamanaka, Yoshiya

PY - 2015/8/18

Y1 - 2015/8/18

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84940754260&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84940754260&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.92.023627

DO - 10.1103/PhysRevA.92.023627

M3 - Article

AN - SCOPUS:84940754260

VL - 92

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 2

M1 - 023627

ER -