### Abstract

The Bogoliubov-de Gennes equations are used for a number of theoretical works on the trapped Bose-Einstein condensates. We consider the case in which these equations have complex eigenvalues. We give the complete set including a pair of complex modes whose eigenvalues are complex conjugate to each other. The expansion of the quantum fields which represent neutral atoms in terms of the complete set brings about the operators associated with the complex modes, which are simply neither bosonic nor fermionic ones. The eigenstate of the Hamiltonian is given. Introducing the notion of the physical states, we discuss the instability of the condensates in the context of Kubo's linear response theory.

Original language | English |
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Pages (from-to) | 331-336 |

Number of pages | 6 |

Journal | Journal of Low Temperature Physics |

Volume | 148 |

Issue number | 3-4 |

DOIs | |

Publication status | Published - 2007 Aug 1 |

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics
- Materials Science(all)
- Condensed Matter Physics

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## Cite this

*Journal of Low Temperature Physics*,

*148*(3-4), 331-336. https://doi.org/10.1007/s10909-007-9393-y