Finite-temperature phase diagram of a spin-1 Bose gas

@article{Kawaguchi2012FinitetemperaturePD,
  title={Finite-temperature phase diagram of a spin-1 Bose gas},
  author={Yuki Kawaguchi and Nguyen Thanh Phuc and P. B. Blakie},
  journal={Physical Review A},
  year={2012},
  volume={85},
  pages={053611}
}
We formulate a self-consistent Hartree-Fock theory for a spin-1 Bose gas at finite temperature and apply it to characterization of the phase diagram. We find that spin coherence between thermal atoms in different magnetic sublevels develops via coherent collisions with the condensed atoms, and is a crucial factor in determining the phase diagram. We develop analytical expressions to characterize the interaction- and temperature-dependent shifts of the phase boundaries. 

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