Abstract
In this article we study the hydrodynamic spectrum of a superfluid confined in cylindrical trap. We show that the dispersion relation of the phonon branch scales like at large q, leading to a vanishingly small superfluid critical velocity. In practice the critical velocity is set by the breakdown of the hydrodynamic approximation. For a broad class of superfluids, this entails a reduction of the critical velocity by a factor with respect to the free-space prediction (here is the trapping frequency and the chemical potential of the cloud).
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