Two possible types of superfluidity in crystals

Using a modified procedure to derive hydrodynamics, it is shown from symmetry considerations that a superfluid velocity v⃗^s which is invariant under a Galilean transformation will be driven by the temperature: v→•^s+(k_B/m)∇⃗T=0. A crystal with such a velocity is able to sustain a persistent entropy flux rather than a mass current and has a propagating mode connected to temperature fluctuations. On the other hand, only a crystal with a v⃗^s which behaves like a true velocity under a Galilean transformation, will be able to sustain a persistent mass current and have vacancy propagation as its Goldstone mode. This spectrum differs, however, from that given by previous authors.