The energy of dilute Bose gases II: The general case

Abstract

For a dilute system of non-relativistic bosons interacting through a positive 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 1960's.

arXiv comment93 pages. Follow-up paper to our previous article arXiv:1904.06164. arXiv admin note: text overlap with arXiv:1904.06164