We provide an upper bound on the ground state energy per unit volume of a dilute Bose gas in the thermodynamic limit capturing the correct second order term, as predicted by the celebrated Lee-Huang-Yang formula. With respect to the first proof of this result, given by H.-T. Yau and J. Yin, our trial state is simpler, it applies to a larger class of interactions and it provides a better rate.

Joint work with S. Cenatiempo and B. Schlein.

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