Free Energies of Dilute Bose Gases: Upper Bound

Jun Yin University of Wisconsin-Madison

Mathematical Physics mathscidoc:1608.22011

Journal of Statistical Physics, 141, (4), 683–726, 2010
We derive an upper bound on the free energy of a Bose gas at density $ \varrho $ and temperature T. In combination with the lower bound derived previously by Seiringer (Commun. Math. Phys. 279(3): 595–636, 2008), our result proves that in the low density limit, i.e., when $ a^3 \varrho \ll 1$, where $a$ denotes the scattering length of the pair-interaction potential, the leading term of $\Delta f$, the free energy difference per volume between interacting and ideal Bose gases, is equal to $ 4\pi a(2\varrho^{2}-[\varrho-\varrho_{c}]^{2}_{+}) $. Here, $\varrho_c (T)$ denotes the critical density for Bose–Einstein condensation (for the ideal Bose gas), and $ [⋅]_{+}= max \{⋅ , 0\}$ denotes the positive part.
Bose gas, Free energy, Variational principle
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@inproceedings{jun2010free,
  title={Free Energies of Dilute Bose Gases: Upper Bound},
  author={Jun Yin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160823233317894280421},
  booktitle={Journal of Statistical Physics},
  volume={141},
  number={4},
  pages={683–726},
  year={2010},
}
Jun Yin. Free Energies of Dilute Bose Gases: Upper Bound. 2010. Vol. 141. In Journal of Statistical Physics. pp.683–726. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160823233317894280421.
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