Free Energies of Dilute Bose gases
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چکیده
We derive a upper bound on the free energy of a Bose gas system at density ̺ and temperature T . In combination with the lower bound derived previously by Seiringer [15], our result proves that in the low density limit, i.e., when a̺ ≪ 1, where a denotes the scattering length of the pair-interaction potential, the leading term of ∆f the free energy difference per volume between interacting and ideal Bose gases is equal to 4πa(2̺ − [̺ − ̺ c]2+). Here, ̺ c(T ) denotes the critical density for Bose-Einstein condensation (for the ideal gas), and [·]+ = max{·, 0} denotes the positive part.
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تاریخ انتشار 2009