### Abstract

We generalize the perturbation theory of weakly interacting bosons to Bose-Einstein condensates with hyperfine spin [Formula Presented] Analytical expressions of second-order self-energies beyond the mean-field approximation are derived at zero temperature. We further extend the perturbation theory to the finite-temperature case, and derive the corresponding self-energies. We evaluate these self-energies near the poles of the first-order (mean-field) Green’s functions within the on-shell approximation, and expand the results in powers of wave number in the long-wavelength limit. Excitation spectra for each mode are obtained analytically at low temperatures. We also derive the ground-state energy and thermodynamic quantities such as free energy of the system.

Original language | English |
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Number of pages | 1 |

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

Volume | 68 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2003 Jan 1 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Physical Review A - Atomic, Molecular, and Optical Physics*,

*68*(1). https://doi.org/10.1103/PhysRevA.68.013601