### Abstract

We construct an approximate scheme based on the concept of the spontaneous symmetry breakdown, satisfying the Goldstone theorem, for finite volume Bose-Einstein condensed gases in both zero and finite temperature cases. In this paper, we discuss the Bose-Einstein condensation in a box with periodic boundary condition and do not assume the thermodynamic limit. When energy spectrum is discrete, we found that it is necessary to deal with the Nambu-Goldstone mode explicitly without the Bogoliubov's prescription, in which zero-mode creation- and annihilation-operators are replaced with a c-number by hand, for satisfying the Goldstone theorem. Furthermore, we confirm that the unitarily inequivalence of vacua in the spontaneous symmetry breakdown is true for the finite volume system.

Original language | English |
---|---|

Pages (from-to) | 1892-1917 |

Number of pages | 26 |

Journal | Annals of Physics |

Volume | 321 |

Issue number | 8 |

DOIs | |

Publication status | Published - 2006 Aug |

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### Keywords

- Bose-Einstein condensation
- Goldstone theorem
- Hugenholtz-Pines theorem
- Spontaneous symmetry breakdown
- Unitarily inequivalent vacua
- Ward-Takahashi relations

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Annals of Physics*,

*321*(8), 1892-1917. https://doi.org/10.1016/j.aop.2005.12.009

**Goldstone theorem, Hugenholtz-Pines theorem, and Ward-Takahashi relation in finite volume Bose-Einstein condensed gases.** / Enomoto, Hiroaki; Okumura, Masahiko; Yamanaka, Yoshiya.

Research output: Contribution to journal › Article

*Annals of Physics*, vol. 321, no. 8, pp. 1892-1917. https://doi.org/10.1016/j.aop.2005.12.009

}

TY - JOUR

T1 - Goldstone theorem, Hugenholtz-Pines theorem, and Ward-Takahashi relation in finite volume Bose-Einstein condensed gases

AU - Enomoto, Hiroaki

AU - Okumura, Masahiko

AU - Yamanaka, Yoshiya

PY - 2006/8

Y1 - 2006/8

N2 - We construct an approximate scheme based on the concept of the spontaneous symmetry breakdown, satisfying the Goldstone theorem, for finite volume Bose-Einstein condensed gases in both zero and finite temperature cases. In this paper, we discuss the Bose-Einstein condensation in a box with periodic boundary condition and do not assume the thermodynamic limit. When energy spectrum is discrete, we found that it is necessary to deal with the Nambu-Goldstone mode explicitly without the Bogoliubov's prescription, in which zero-mode creation- and annihilation-operators are replaced with a c-number by hand, for satisfying the Goldstone theorem. Furthermore, we confirm that the unitarily inequivalence of vacua in the spontaneous symmetry breakdown is true for the finite volume system.

AB - We construct an approximate scheme based on the concept of the spontaneous symmetry breakdown, satisfying the Goldstone theorem, for finite volume Bose-Einstein condensed gases in both zero and finite temperature cases. In this paper, we discuss the Bose-Einstein condensation in a box with periodic boundary condition and do not assume the thermodynamic limit. When energy spectrum is discrete, we found that it is necessary to deal with the Nambu-Goldstone mode explicitly without the Bogoliubov's prescription, in which zero-mode creation- and annihilation-operators are replaced with a c-number by hand, for satisfying the Goldstone theorem. Furthermore, we confirm that the unitarily inequivalence of vacua in the spontaneous symmetry breakdown is true for the finite volume system.

KW - Bose-Einstein condensation

KW - Goldstone theorem

KW - Hugenholtz-Pines theorem

KW - Spontaneous symmetry breakdown

KW - Unitarily inequivalent vacua

KW - Ward-Takahashi relations

UR - http://www.scopus.com/inward/record.url?scp=33745501681&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33745501681&partnerID=8YFLogxK

U2 - 10.1016/j.aop.2005.12.009

DO - 10.1016/j.aop.2005.12.009

M3 - Article

AN - SCOPUS:33745501681

VL - 321

SP - 1892

EP - 1917

JO - Annals of Physics

JF - Annals of Physics

SN - 0003-4916

IS - 8

ER -