In a recent paper1 it was argued that rotons in superfluid helium 4 are the soft modes announcing a charge density wave that leads to the crystal: rotons are a normal state property. A small superfluid condensate acts to hybridize quasiparticles and soft density fluctuations - hence a level repulsion that lowers the energy: superfluidity is energetically favourable. A shallow roton implies a very small condensate density, as found in He4: what we need is a saturation mechanism. The clue is depletion due to quantum fluctuations. In (1) we assumed that such a depletion was drawn from the condensate itself: superfluidity then disappears in the liquid if the roton gap is too small. Here we explore an alternate possibility: quantum fluctuations are drawn from the normal fluid. We reach the opposite conclusion: superfluidity persists down to the spinodal limit where the roton gap vanishes, with an unusual power law dependence. We briefly mention the possible extension of that argument to a frozen charge density wave: in a toy 1d model it might shed light on the features that favour supersolids.
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Nozières, P. More about Rotons in Superfluid Helium 4. J Low Temp Phys 142, 91–99 (2006). https://doi.org/10.1007/s10909-005-9413-8
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DOI: https://doi.org/10.1007/s10909-005-9413-8