# The Second Order Upper Bound for the Ground Energy of a Bose Gas

 Title: The Second Order Upper Bound for the Ground Energy of a Bose Gas Author: Yau, Horng-Tzer; Yin, Jun Note: Order does not necessarily reflect citation order of authors. Citation: Yau, 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. Full Text & Related Files: 0903.5347v2.pdf (509.5Kb; PDF) Abstract: Consider $$N$$ 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. Published Version: doi:10.1007/s10955-009-9792-3 Other Sources: http://arxiv.org/abs/arXiv:0903.5347 Terms of Use: This article is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#OAP Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:8311970 Downloads of this work: