Resolving the puzzle of sound propagation in liquid helium at low temperatures
Tony C. Scott
Institut für Physikalische Chemie, RWTH Aachen University, Aachen 52056, Germany BlockFint, 139 Sethiwan Tower, 4A Pan Rd, Bangkok 10500, Thailand
Konstantin G. Zloshchastiev
Institute of Systems Science, Durban University of Technology, P.O. Box 1334, Durban 4000, South Africa
Received June 7, 2019, published online October 25, 2019
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.
Key words: superfluid helium, quantum Bose liquid, equation of state, speed of sound.