Correlations in a Repulsive Dilute Fermi Gas

Abstract: In recent years, dilute quantum gases have attracted considerable interest from the mathematical and experimental physics communities, partly due to advances in ultracold atomic gas experiments. A key challenge in mathematical physics is to understand, from first principles, how interactions give rise to correlations between particles and shape the ground state of a many-body system.

In 1957, Huang and Yang predicted an asymptotic formula for the ground state energy of a dilute Fermi gas. This formula captures the effect of correlations and exhibits remarkable universality: to the order considered, the details of the interaction enter through a single parameter, the scattering length. In a recent joint work with C. Hainzl, P. T. Nam, and R. Seiringer, we provided a rigorous proof of this formula.

This talk will introduce the physical context, emphasise the importance of correlations, and outline the key concepts underlying the proof of the Huang–Yang formula. Finally, we will discuss open problems and possible extensions of this work.