Scott T.C., Zloshchastiev K.G. «Resolving the puzzle of sound propagation in liquid helium at low temperatures» Физика низких температур, 45, № 12, с. 1456-1461 (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. Ключевые слова: сверхтекучий гелий, квантовая бозе-жидкость, уравнение состояния, скорость звука.