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The definition of Landau critical velocity is $v_L=\min_{q}\{\frac{\omega(q)}{q}\}$, where $\omega(q)$ is the spectrum of excitations. The viscosity vanishes when the object is moving through the superfluid with velocity less than $v_L$. And the sound velocity is the speed of perturbed density, which can be defined as $\lim_{q\to 0\frac{\omega_q}{q}}$.

Are the Landau critical velocity and sound velocity the same in the superfluid?

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  • $\begingroup$ It's currently unclear what exactly this question is asking. Please add further information about the context so that potential answerers will know exactly what the issue here is, in particular explain the definitions of "Landau velocity" and "sound velocity" you're working with. $\endgroup$ – ACuriousMind Dec 12 '17 at 13:34
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In the case of spectrum with roton, they are not the same.

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