Resolving the puzzle of sound propagation in liquid helium at low temperatures

TL;DR

This paper explains the peculiar sound propagation in low-temperature liquid helium by modeling it as a mixture of three quantum Bose liquids, deriving an equation of state and sound speed that match experimental data.

Contribution

It introduces a novel quantum wave equation with polynomial and logarithmic nonlinearities to model liquid helium's behavior at low temperatures.

Findings

Derived an equation of state consistent with experimental data.

Predicted the speed of sound approaching zero near a critical pressure.

Provided a unified quantum model explaining cavitation instability.

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 (Gross-Pitaevskii-type) Bose-Einstein condensate, Ginzburg-Sobyanin-type fluid, and logarithmic superfluid. Therefore, the dynamics of such a mixture is described by a quantum wave equation, which contains not only the polynomial (Gross-Pitaevskii and Ginzburg-Sobyanin) nonlinearities with respect to a condensate wavefunction, but also a non-polynomial logarithmic nonlinearity. We derive an equation of state and speed of sound in our model, and show their agreement with experiment.