Yau, Horng-TzerYin, Jun2012-03-052009Yau, Horng-Tzer, and Jun Yin. 2009. The second order upper bound for the ground energy of a Bose gas. Journal of Statistical Physics 136(3): 453-503.1572-9613http://nrs.harvard.edu/urn-3:HUL.InstRepos:8311970Consider \(N\) bosons in a finite box \(\Lambda= [0,L]^3\subset \mathbf R^3\) interacting via a two-body smooth repulsive short range potential. We construct a variational state which gives the following upper bound on the ground state energy per particle \[\overline\lim_{\rho\to0} \overline\lim_{L \to \infty, N/L^3 \to \rho} \left(\frac{e_0(\rho)- 4 \pi a \rho}{(4 \pi a)^{5/2}(\rho)^{3/2}}\right)\leq \frac{16}{15\pi^2}, \] where \(a\) is the scattering length of the potential. Previously, an upper bound of the form \(C 16/15\pi^2\) for some constant \(C > 1\) was obtained in. Our result proves the upper bound of the the prediction by Lee-Yang and Lee-Huang-Yang.en-USBose gasBogoliubov transformationvariational principleJournal Article2012-03-0510.1007/s10955-009-9792-3