TY - JOUR

T1 - The energy of dilute Bose gases II

T2 - the general case

AU - Fournais, Søren

AU - Solovej, Jan Philip

N1 - Funding Information: SF was partially supported by a Sapere Aude grant from the Independent Research Fund Denmark, Grant number DFF–4181-00221, by the Charles Simonyi Endowment, and by an EliteResearch Prize from the Danish Ministry of Higher Education and Science. JPS was partially supported by the Villum Centre of Excellence for the Mathematics of Quantum Theory (QMATH). Publisher Copyright: © 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2023

Y1 - 2023

N2 - 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(ρ)≥4πaρ2(1+12815πρa3+o(ρa3)), thereby proving a lower bound consistent with the Lee–Huang–Yang formula for the energy density. The proof allows for potentials with large L1-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.

AB - 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(ρ)≥4πaρ2(1+12815πρa3+o(ρa3)), thereby proving a lower bound consistent with the Lee–Huang–Yang formula for the energy density. The proof allows for potentials with large L1-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.

U2 - 10.1007/s00222-022-01175-0

DO - 10.1007/s00222-022-01175-0

M3 - Journal article

AN - SCOPUS:85143829824

VL - 232

SP - 863

EP - 994

JO - Inventiones Mathematicae

JF - Inventiones Mathematicae

SN - 0020-9910

ER -