### Abstract

The Bogoliubov-de Gennes equations are used for a number of theoretical works to describe quantum and thermal fluctuations of trapped Bose-Einstein condensates. We consider the case in which the condensate has a highly quantized vortex. It is known that these equations have complex eigenvalues in this case. We give the complete set including a pair of complex modes whose eigenvalues are complex conjugates to each other. The expansion of the quantum fields which represent neutral atoms in terms of the complete set brings 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) | 211-214 |

Number of pages | 4 |

Journal | Laser Physics |

Volume | 17 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2007 Feb |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics
- Physics and Astronomy (miscellaneous)

### Cite this

**Quantum field theoretical description of unstable behavior of a Bose-Einstein condensate with a highly quantized vortex in a harmonic potential.** / Okumura, M.; Mine, Makoto; Sunaga, T.; Yamanaka, Yoshiya.

Research output: Contribution to journal › Article

*Laser Physics*, vol. 17, no. 2, pp. 211-214. https://doi.org/10.1134/S1054660X07020272

}

TY - JOUR

T1 - Quantum field theoretical description of unstable behavior of a Bose-Einstein condensate with a highly quantized vortex in a harmonic potential

AU - Okumura, M.

AU - Mine, Makoto

AU - Sunaga, T.

AU - Yamanaka, Yoshiya

PY - 2007/2

Y1 - 2007/2

N2 - The Bogoliubov-de Gennes equations are used for a number of theoretical works to describe quantum and thermal fluctuations of trapped Bose-Einstein condensates. We consider the case in which the condensate has a highly quantized vortex. It is known that these equations have complex eigenvalues in this case. We give the complete set including a pair of complex modes whose eigenvalues are complex conjugates to each other. The expansion of the quantum fields which represent neutral atoms in terms of the complete set brings 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.

AB - The Bogoliubov-de Gennes equations are used for a number of theoretical works to describe quantum and thermal fluctuations of trapped Bose-Einstein condensates. We consider the case in which the condensate has a highly quantized vortex. It is known that these equations have complex eigenvalues in this case. We give the complete set including a pair of complex modes whose eigenvalues are complex conjugates to each other. The expansion of the quantum fields which represent neutral atoms in terms of the complete set brings 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.

UR - http://www.scopus.com/inward/record.url?scp=33847233971&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33847233971&partnerID=8YFLogxK

U2 - 10.1134/S1054660X07020272

DO - 10.1134/S1054660X07020272

M3 - Article

AN - SCOPUS:33847233971

VL - 17

SP - 211

EP - 214

JO - Laser Physics

JF - Laser Physics

SN - 1054-660X

IS - 2

ER -