The energy of dilute Bose gases II: the general case

Abstract

For a dilute system of non-relativistic bosons in 3 dimensions interacting through a positive, radially symmetric, potential v with scattering length a we prove that the ground state energy density satisfies the bound \(e(\rho ) \ge 4\pi a \rho ^2 (1+ \frac{128}{15\sqrt{\pi }} \sqrt{\rho a^3} +o(\sqrt{\rho a^3}\,))\), thereby proving a lower bound consistent with the Lee–Huang–Yang formula for the energy density. The proof allows for potentials with large \(L^1\)-norm, in particular, the case of hard core interactions is included. Thereby, we solve a problem in mathematical physics that had been a major challenge since the 1950’s.