The energy of dilute Bose gases II: The general case

DOI10.1007/S00222-022-01175-0arXiv2108.12022MaRDI QIDQ6376106

S. Fournais, Jan Philip Solovej

Publication date: 26 August 2021

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 $e(ho)geq4piah{o}^2(1+frac12815sqrtpisqrtho{a}^3+o(sqrtho{a}^3,))$, 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.

Mathematics Subject Classification ID

Equilibrium statistical mechanics (82Bxx) Applications of statistical mechanics to specific types of physical systems (82Dxx) Applications of quantum theory to specific physical systems (81Vxx)

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