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Three fermions with strongly repulsive interactions in a spherical harmonictrap, constitute the simplest nontrivial system that can exhibit the onset ofitinerant ferromagnetism. Here, we present exact solutions for three trapped,attractively interacting fermions near a Feshbach resonance. We analyze energylevels on the upper branch of the resonance where the atomic interaction iseffectively repulsive. When the s-wave scattering length a is sufficientlypositive, three fully polarized fermions are energetically stable against asingle spin-flip, indicating the possibility of itinerant ferromagnetism, asinferred in the recent experiment. We also investigate the high-temperaturethermodynamics of a strongly repulsive or attractive Fermi gas using a quantumvirial expansion. The second and third virial coefficients are calculated. Theresulting equations of state can be tested in future quantitative experimentalmeasurements at high temperatures and can provide a useful benchmark forquantum Monte Carlo simulations.

Three attractively interacting fermions in a harmonic trap: Exact solution, ferromagnetism, and high-temperature thermodynamics