Comment on ``Sound velocity and multibranch Bogoliubov spectrum of an elongated Fermi superfluid in the BEC-BCS crossover'

摘要

The work by T. K. Ghosh and K. Machida [cond-mat/0510160 and Phys. Rev. A 73,013613 (2006)] on the sound velocity in a cylindrically confined Fermisuperfluid obeying a power-law equation of state is shown to make use of animproper projection of the sound wave equation. This inaccuracy fully accountsfor the difference between their results and those previously reported byCapuzzi et al. [cond-mat/0509323 and Phys. Rev. A 73, 021603(R) (2006)]. Inthis Comment we show that both approaches lead exactly to the same result whenthe correct weight function is used in the projection. Plots of the correctbehavior of the phonon and monopole-mode spectra in the BCS, unitary, and BEClimits are also shown.