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

TL;DR

This paper clarifies the correct method for calculating sound velocity and excitation spectra in elongated Fermi superfluids across the BEC-BCS crossover, correcting previous inaccuracies and reconciling different approaches.

Contribution

It demonstrates the proper projection method for sound wave equations in Fermi superfluids, resolving discrepancies in prior theoretical results.

Findings

Corrected the projection method yields results consistent with previous studies.

Plots of phonon and monopole-mode spectra across BEC-BCS limits are provided.

Clarified the theoretical approach for sound velocity calculations in Fermi superfluids.

Abstract

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 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. [cond-mat/0509323 and Phys. Rev. A 73, 021603(R) (2006)]. 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, unitary, and BEC limits are also shown.