2. Delta Fermi gasOne aims at a better understanding of the ground state for a delta Fermi gas, which might help to prove (enhanced) area laws.
Problem 2.1.The weak coupling asymptotics of the ground state energy-density for the delta Fermi gas with frozen spin leads to the asymptotic analysis of the Gaudin integral equation. For sectors of non-zero spin one arrives at a system of coupled integral equations, which one could possibly analyse in a similar fashion.
Problem 2.2.For the Fermi gas with delta pair interaction, is there a characterization of the grounds state correlation functions in terms of a two(?)-particle operator, similar to the determinantal description in the case of free Fermions?
Cite this as: AimPL: Fisher-Hartwig asymptotics and Szego expansions, available at http://aimpl.org/fhszego.