The energy of dilute Bose gases

Abstract

For a dilute system of non-relativistic bosons interacting through a positive, compactly supported, $L^1$-potential $v$ with scattering length $a$ we prove that the ground state energy density satisfies the bound $e(\rho ) \geq 4\pi a \rho ^2 (1+ \frac {128}{15\sqrt {\pi }} \sqrt {\rho a^3} +o(\sqrt {\rho a^3}))$, thereby proving the Lee-Huang-Yang formula for the energy density.