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We consider a dilute Bose gas in the thermodynamic limit and prove a lower bound on the free energy for low temperatures which is in agreement with the conjecture of Lee-Huang-Yang on the excitation spectrum of the system. Combining techniques of FS2 and HHNST, we give a simpler and shorter proof resolving the case of strong interactions, including the hard-core potential.
Fournais et al. (Mon,) studied this question.
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