Resolving the puzzle of sound propagation in liquid helium at low temperatures
Abstract
Experimental data suggests that, at temperatures below 1 K, the pressure in liquid helium has a cubic dependence on density. Thus the speed of sound scales as a cubic root of pressure. Near a critical pressure point, this speed approaches zero whereby the critical pressure is negative, thus indicating a cavitation instability regime. We demonstrate that to explain this dependence, one has to view liquid helium as a mixture of three quantum Bose liquids: dilute (GrossPitaevskiitype) BoseEinstein condensate, GinzburgSobyanintype fluid, and logarithmic superfluid. Therefore, the dynamics of such a mixture is described by a quantum wave equation, which contains not only the polynomial (GrossPitaevskii and GinzburgSobyanin) nonlinearities with respect to a condensate wavefunction, but also a nonpolynomial logarithmic nonlinearity. We derive an equation of state and speed of sound in our model, and show their agreement with the experiment.
 Publication:

Low Temperature Physics
 Pub Date:
 December 2019
 DOI:
 10.1063/10.0000200
 arXiv:
 arXiv:2006.08981
 Bibcode:
 2019LTP....45.1231S
 Keywords:

 Condensed Matter  Quantum Gases;
 Physics  Fluid Dynamics
 EPrint:
 5 pages, 3 figures, final/published version