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

Tony C. Scott; Konstantin G. Zloshchastiev

doi:10.1063/10.0000200

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arXiv · 2006.08981

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

Tony C. Scott·Konstantin G. Zloshchastiev

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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.

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Tony C. Scott, Konstantin G. Zloshchastiev. 2020-06-16. Resolving the puzzle of sound propagation in liquid helium at low temperatures. https://doi.org/10.1063/10.0000200

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