Work

The Huang–Yang Formula for the Low‐Density Fermi Gas: Upper Bound

Year: 2026

Type: article

Abstract: ABSTRACT We study the ground state energy of a gas of spin fermions with repulsive short‐range interactions. We derive an upper bound that agrees, at low density , with the Huang–Yang conjecture. The latter captures the first three terms in an asymptotic low‐density expansion, and in particular the Huang–Yang correction term of order . Our trial state is constructed using an adaptation of the bosonic Bogoliubov theory to the Fermi system, where the correlation structure of fermionic particles is incorporated by quasi‐bosonic Bogoliubov transformations. In the latter, it is important to consider a modified zero‐energy scattering equation that takes into account the presence of the Fermi sea, in the spirit of the Bethe–Goldstone equation.

Source: Communications on Pure and Applied Mathematics

DOI: 10.1002/cpa.70040

Authors: Emanuela L. Giacomelli, Christian Hainzl, Phan Thành Nam, Robert Seiringer

Institutions: University of Milan, Ludwig-Maximilians-Universität München, Institute of Science and Technology Austria

Language: English

Topic: Cold Atom Physics and Bose-Einstein Condensates

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $5,230

Funders: Università degli Studi di Milano, Deutsche Forschungsgemeinschaft, European Research Council