### Abstract

We study the dynamics of a trapped Bose-Einstein condensate with a multiply-quantized vortex, and investigate the roles of the fluctuations in the dynamical evolution of the system. Using the perturbation theory of the external potential, and assuming the situation of the small coupling constant of self-interaction, we analytically solve the time-dependent Gross-Pitaevskii equation. We introduce the zero mode and its adjoint mode of the Bogoliubov-de Gennes equations. Those modes are known to be essential for the completeness condition. We confirm how the complex eigenvalues induce the vortex splitting. It is shown that the physical role of the adjoint zero mode is to ensure the conservation of the total condensate number. The contribution of the adjoint mode is exponentially enhanced in synchronism with the exponential growth of the complex mode, and is essential in the vortex splitting.

Original language | English |
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Pages (from-to) | 2359-2371 |

Number of pages | 13 |

Journal | Annals of Physics |

Volume | 324 |

Issue number | 11 |

DOIs | |

Publication status | Published - 2009 Nov 1 |

### Keywords

- 03.75.Kk
- 03.75.Lm
- 05.30.Jp
- Bose-Einstein condensation
- Dynamical instability
- Quantized vortex
- Zero mode

### ASJC Scopus subject areas

- Physics and Astronomy(all)

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## Cite this

*Annals of Physics*,

*324*(11), 2359-2371. https://doi.org/10.1016/j.aop.2009.07.004