A Simple 2nd Order Lower Bound to the Energy of Dilute Bose Gases

For a dilute system of non-relativistic bosons interacting through a positive, radial potential v with scattering length a we prove that the ground state energy density satisfies the bound e(ρ)≥4πaρ2(1-Cρa3). BB and JPS were partially supported by the Villum Centre of Excellence for the Mathematics of Quantum Theory (QMATH) and the ERC Advanced Grant 321029. BB also gratefully acknowledges support from the DFG under Germany’s Excellence Strategy EXC-2181/1 - 390900948 and Grant No. AOBJ 643360 KN 102013-1. SF was partially supported by a Sapere Aude Grant from the Independent Research Fund Denmark, Grant No. DFF–4181-00221.