Free Energies of Dilute Bose Gases: Upper Bound |
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Authors: | Jun Yin |
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Institution: | 1.Department of Mathematics, FAS,Harvard University,Cambridge,USA |
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Abstract: | We derive an upper bound on the free energy of a Bose gas at density ϱ 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
ϱ≪1, where a denotes the scattering length of the pair-interaction potential, the leading term of Δf, the free energy difference per volume between interacting and ideal Bose gases, is equal to 4pa(2r2-r-rc]2+)4\pi a(2\varrho^{2}-\varrho-\varrho_{c}]^{2}_{+}). Here, ϱ
c
(T) denotes the critical density for Bose–Einstein condensation (for the ideal Bose gas), and ⋅]+=max {⋅,0} denotes the positive part. |
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