The ground state energy density of a dilute Bose gas is rigorously shown to be at most the Lee-Huang-Yang value plus Wu's logarithmic third-order correction, for potentials with positive scattering length.
Third order corrections to the ground state energy of a Bose gas in the Gross-Pitaevskii regime
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For a translation invariant system of $N$ bosons in the Gross-Pitaevskii regime, we establish a precise bound for the ground state energy $E_N$. While the leading, order $N$, contribution to $E_N$ has been known since [30,28] and the second order corrections (of order one) have been first determined in [5], our estimate also resolves the next term in the asymptotic expansion of $E_N$, which is of the order $(\log N) / N$.
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Third Order Upper Bound for the Ground State Energy of the Dilute Bose Gas
The ground state energy density of a dilute Bose gas is rigorously shown to be at most the Lee-Huang-Yang value plus Wu's logarithmic third-order correction, for potentials with positive scattering length.