The energy of dilute Bose gases II: the general case

• 成果类型: Article
• 署名作者: Fournais, Soren; Solovej, Jan Philip
• 署名单位: Aarhus University; University of Copenhagen
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-022-01175-0
• 发表日期: 2023
• 页码: 863-994
• 关键词: ground-state energy

摘要

For a dilute system of non-relativistic bosons in 3 dimensions inter-acting through a positive, radially symmetric, potential v with scattering length a we prove that the ground state energy density satisfies the bound e(rho) >= 4 pi a rho(2)(1+128/15 root pi root rho a(3)+o(root rho a(3))), thereby proving a lower bound consistent with the Lee-Huang-Hang formula for the energy density. The proof allows for potentials with largeL1-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.