### Abstract

We compare many-body theories describing fluctuation corrections to the mean-field theory in a weakly interacting Bose-condensed gas. Using a generalized random-phase approximation, we include both density fluctuations and fluctuations in the particle-particle scattering channel in a consistent manner. We also separately examine effects of the fluctuations within the framework of the random-phase approximation. Effects of fluctuations in the particle-particle scattering channel are also separately examined by using the many-body T-matrix approximation. We assess these approximations with respect to the transition temperature T_{c}, the order of phase transition, as well as the so-called Nepomnyashchii-Nepomnyashchii identity, which states the vanishing off-diagonal self-energy in the low-energy and low-momentum limit. Since the construction of a consistent theory for interacting bosons which satisfies various required conditions is a long-standing problem in cold atom physics, our results would be useful for this important challenge.

Original language | English |
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Article number | 053633 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 88 |

Issue number | 5 |

DOIs | |

Publication status | Published - 26 Nov 2013 |