The energy of dilute Bose gases II: the general case

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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.

Original languageEnglish
JournalInventiones Mathematicae
Pages (from-to)863–994
Publication statusPublished - 2023

Bibliographical note

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.

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