### Abstract

The formulation for zero mode of a Bose–Einstein condensate beyond the Bogoliubov approximation at zero temperature [Y. Nakamura et al., Phys. Rev. A 89 (2014) 013613] is extended to finite temperature. Both thermal and quantum fluctuations are considered in a manner consistent with a concept of spontaneous symmetry breakdown for a finite-size system. Therefore, we need a proper treatment of the zero mode operators, which invoke non-trivial enhancements in depletion condensate and thermodynamical quantities such as the specific heat. The enhancements are visible in the weak interaction case. Our approach reproduces the results of a homogeneous system in the Bogoliubov approximation in a large particle number limit.

Original language | English |
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Pages (from-to) | 484-498 |

Number of pages | 15 |

Journal | Annals of Physics |

Volume | 376 |

DOIs | |

Publication status | Published - 2017 Jan 1 |

### Keywords

- Bose–Einstein condensation
- Cold atom
- Finite temperature
- Quantum field theory
- Spontaneous symmetry breaking
- Zero mode

### ASJC Scopus subject areas

- Physics and Astronomy(all)

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## Cite this

*Annals of Physics*,

*376*, 484-498. https://doi.org/10.1016/j.aop.2016.12.020