2019/12/01 by Tony C. Scott, Konstantin G. Zloshchastiev · 2 citations
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Mechanical and Optical Resonators #Quantum, superfluid, helium dynamics #cond-mat.quant-gas #physics.flu-dyn
paper · pdf · doi:10.1063/10.0000200
published as Low Temp. Phys. 45, 1231 (2019) · 5 pages, 3 figures, final/published version
openalex publication_date 2019/12/01 · openalex created_date 2020/01/10 · arxiv created 2020/06/16 · arxiv updated 2020/06/17 · openalex updated_date 2026/07/28
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.