The interaction-sensitive states of a trapped two-component ideal Fermi gas and application to the virial expansion of the unitary Fermi gas

Abstract : We consider a two-component ideal Fermi gas in an isotropic harmonic potential. Some eigenstates have a wavefunction that vanishes when two distinguishable fermions are at the same location, and would be unaffected by s-wave contact interactions between the two components. We determine the other, interaction-sensitive eigenstates, using a Faddeev ansatz. This problem is nontrivial, due to degeneracies and to the existence of unphysical Faddeev solutions. As an application we present a new conjecture for the fourth-order cluster or virial coefficient of the unitary Fermi gas, in good agreement with the numerical results of Blume and coworkers.
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Shimpei Endo, Yvan Castin. The interaction-sensitive states of a trapped two-component ideal Fermi gas and application to the virial expansion of the unitary Fermi gas. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2016, 49, pp.265301. ⟨10.1088/1751-8113/49/26/265301⟩. ⟨hal-01246611v4⟩

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