A comment on the letter by M. Machida and T. Koyama, Phys. Rev. Lett. {\bf 94}, 140401 (2005) and also on the preprint by Y. Kawaguchi and T. Ohmi, cond-mat/0411018.
The work by T. K. Ghosh and K. Machida [Phys. Rev. A 73, 013613 (2006) and cond-mat/0510160] on the sound velocity in a cylindrically confined Fermi superfluid obeying a power-law equation of state is shown to make use of an improper projection of the sound wave equation. This inaccuracy fully accounts for the difference between their results and those previously reported by Capuzzi et al. [Phys. Rev. A 73, 021603(R) (2006) and cond-mat/0509323]. In this Comment, we show that both approaches lead exactly to the same result when the correct weight function is used in the projection. Plots of the correct behavior of the phonon and monopole-mode spectra in the BCS and unitary limits and in the BEC regime are also shown.
The model which we have recently proposed to describe the behavior of a dilute Fermi gas in the presence of a Fechbach resonance (M. Holland, S.J.J.M.F. Kokkelmans, M.L. Chiofalo, and R. Walser, Phys. Rev. Lett. 87), 120406 (2001). (S.J.J.M.F. Kokkelmans, J.N. Milstein, M.L. Chiofalo, R. Walser, and M.J. Holland, e-print cond-mat/0112283.) has been extended to take into account the first order effects of pairing fluctuations. Within the context of a path integral formalism, we discuss a model which describes the crossover between the strong and weak coupling regimes of a dilute Fermi gas in the presence of a Feschbach resonance. With this model we are able to connect between the weak coupling BCS-regime and the strongly coupled BEC limits by modifying the detuning of the resonant state. Even though the scattering length goes through a singularity in the intermediate coupling regime, the curves connecting these regimes remains smooth.