Equation of state and collective frequencies of a trapped Fermi gas   along the BEC-unitarity crossover
  We show that the study of the collective oscillations in a harmonic trap provides a very sensitive test of the equation of state of a Fermi gas near a Feshbach resonance. Using a scaling approach, whose high accuracy is proven by comparison with exact hydrodynamic solutions, the frequencies of the lowest compressional modes are calculated at T=0 in terms of a dimensionless parameter characterizing the equation of state. The predictions for the collective frequencies, obtained from the equations of state of mean field BCS theory and of recent Monte-Carlo calculations, are discussed in detail. 
G.E. Astrakharchik, R. Combescot, X. Leyronas and S. Stringari