# Why water is not superfluid?

My question is in the title. I do not really understand why water is not a superfluid. Maybe I make a mistake but the fact that water is not suprfluid comes from the fact that the elementary excitations have a parabolic dispersion curve but for me the question remain. An equivalent way to ask it is: why superfluid helium is described by Gross-Pitaevsky equation and it is not the case for water?

• Recent work actually suggests that water may have a superfluid liquid phase
– user20145
Jan 23, 2013 at 15:24
• @x you have to substantiate this claim by a reference or link and a quote, at least from the abstract. Jan 23, 2013 at 15:31

You refer to the Landau criterion for superfluidity (there is a separate question whether this is really the best way to think about superfluids, and whether the Landau criterion is necessary and/or sufficient). In a superfluid the low energy excitations are phonons, the dispersion relation is linear $E_p\sim c p$, and the critical velocity is non-zero. In water the degrees of freedom are water molecules, the dispersion relation is quadratic, $E_p\sim p^2/(2m)$, and the critical velocity is zero.
• A rough criterion is the condition for Bose condensation in an ideal gas, $n\lambda^3\sim 1$, where $n$ is the density and $\lambda$ is the thermal wave length. Note that your question is in some sense backwards: Helium is the exception, water is the rule. Most ordinary fluids solidify instead of becoming superfluid at low $T$. Sep 24, 2012 at 12:38
• I'm not sure that one should consider ordinary molecules as quasiparticles leading to dissipation because the Landau criterion originates from investigation of a phonon branch. Instead, we have to use the same formalism of phonons to be able to compare liquids' behavior. In non-superconducting liquid a phonon dispersion law is $E=c|p|$. So applying Landau criterion we obtain a peculiar critical velocity equal to $c$ - the speed of sound. It doesn't mean necessarily that the liquid is superconducting below $c$. It rather means that it goes into a different state above $c$ (supersonic flow). Jul 6, 2020 at 19:27