### 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 language | English |
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Pages (from-to) | 250-260 |

Number of pages | 11 |

Journal | Annals of Physics |

Volume | 347 |

DOIs | |

Publication status | Published - 2014 |

### Fingerprint

### 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.

Research output: Contribution to journal › Article

*Annals of Physics*, vol. 347, pp. 250-260. https://doi.org/10.1016/j.aop.2014.05.004

}

TY - JOUR

T1 - Dynamical instability induced by the zero mode under symmetry breaking external perturbation

AU - Takahashi, Junichi

AU - Nakamura, Y.

AU - Yamanaka, Yoshiya

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - Bose-Einstein condensation

KW - Dark soliton

KW - Dynamical instability

KW - Zero mode

UR - http://www.scopus.com/inward/record.url?scp=84901357846&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84901357846&partnerID=8YFLogxK

U2 - 10.1016/j.aop.2014.05.004

DO - 10.1016/j.aop.2014.05.004

M3 - Article

VL - 347

SP - 250

EP - 260

JO - Annals of Physics

JF - Annals of Physics

SN - 0003-4916

ER -