Resolving the puzzle of sound propagation in liquid helium at low temperatures
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Date
2019-12
Authors
Scott, Tony C.
Zloshchastiev, Konstantin G.
Journal Title
Journal ISSN
Volume Title
Publisher
AIP Publishing
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 the experiment.
Description
Keywords
Superfluid helium, Quantum Bose liquid, Equation of state, Speed of sound, Cond-mat.quant-gas, Physics.flu-dyn, 0105 Mathematical Physics, 0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics, 0204 Condensed Matter Physics, General Physics, 5102 Atomic, molecular and optical physics, 5104 Condensed matter physics
Citation
Scott, T.C. and Zloshchastiev, K.G. 2019. Resolving the puzzle of sound propagation in liquid helium at low temperatures. Low Temperature Physics. 45(12): 1231-1236. doi:10.1063/10.0000200
DOI
10.1063/10.0000200