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

@article{Scott2019ResolvingTP,
title={Resolving the puzzle of sound propagation in liquid helium at low temperatures},
author={Tony C. Scott and Konstantin G. Zloshchastiev},
journal={arXiv: Quantum Gases},
year={2019}
}
• Published 31 December 2019
• Physics
• arXiv: Quantum Gases
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…
8 Citations

## Figures from this paper

Logarithmic wave-mechanical effects in polycrystalline metals: theory and experiment
• Materials Science
Indian Journal of Physics
• 2021
Schrodinger-type wave equations with logarithmic nonlinearity occur in hydrodynamic models of Korteweg-type materials with capillarity and surface tension, which can undergo liquid–solid or
Resolving cosmological singularity problem in logarithmic superfluid theory of physical vacuum
Recently proposed statistical mechanics arguments [1] and previously known Madelung hydrodynamical presentation of condensate functions [2] have revealed that the quantum liquids with logarithmic
Particle size and phase equilibria in classical logarithmic fluid
• Physics
• 2021
An interparticle interaction potential has been recently proposed in studies of condensate-like systems described by logarithmically nonlinear equations, such as the superfluid helium-4 and
On Asymptotic Behavior of Galactic Rotation Curves in Superfluid Vacuum Theory
Abstract The logarithmic superfluid theory of physical vacuum predicts that gravity is an induced phenomenon, which has a multiple-scale structure. At astronomical scales, as the distance from a
An Alternative to Dark Matter and Dark Energy: Scale-Dependent Gravity in Superfluid Vacuum Theory
We derive an effective gravitational potential, induced by the quantum wavefunction of a physical vacuum of a self-gravitating configuration, while the vacuum itself is viewed as the superfluid
Kink solutions in logarithmic scalar field theory: Excitation spectra, scattering, and decay of bions
• Physics
Physics Letters B
• 2021
Ekaterina Belendryasova, 2, ∗ Vakhid A. Gani, 3, † and Konstantin G. Zloshchastiev ‡ A.A. Bochvar High-Technology Scientific Research Institute for Inorganic Materials (VNIINM), Moscow 123098, Russia
Regularised Finite Difference Methods for the Logarithmic Klein-Gordon Equation
Two regularised finite difference methods for the logarithmic Klein-Gordon equation are studied. In order to deal with the origin singularity, we employ regularised logarithmic Klein-Gordon equations

## References

SHOWING 1-10 OF 82 REFERENCES
Thermodynamic Properties of Superfluid 4He at Negative Pressure
• Physics
• 2002
We calculate the thermodynamics of superfluid 4He at negative pressures. We use the Landau theory in which thermodynamic properties are expressed as sums over the thermal distribution of elementary
VELOCITY OF SOUND IN LIQUID HELIUM AT LOW TEMPERATURES
The velocity of ordinary sound in liquid helium was measured at a frequency of 1 Mc/sec between 0.1 deg K and 1.7 deg K. The observed change in velocity between the lowest temperatures and 1.6 deg K
Superfluidity of helium II near the λ point
• Physics
• 1976
The properties (and particularly the superfluidity) of liquid helium near the λ point have long been and still are objects of numerous investigations. Nonetheless, much of the problem remains
Sound propagation, density, and viscosity in liquid3He
• Physics
• 1972
We have measured the temperature dependence of the velocity and the attenuation of sound in the range 60–700 mK. The maximum in the sound velocity observed by Abraham and Osborne is confirmed. The
Nonlinear wave-mechanical effects in Korteweg fluid magma transport
Statistical mechanics arguments and Madelung hydrodynamical presentation are applied to the transport of magma in volcanic conduits. An effective wave equation with logarithmic nonlinearity becomes
Quantum Bose liquids with logarithmic nonlinearity: self-sustainability and emergence of spatial extent
• Physics
• 2011
The Gross–Pitaevskii (GP) equation is a long-wavelength approach widely used to describe the dilute Bose–Einstein condensates (BEC). However, in many physical situations, such as higher densities, it
Stability and Metastability of Trapless Bose-Einstein Condensates and Quantum Liquids
Abstract Various kinds of Bose-Einstein condensates are considered, which evolve without any geometric constraints or external trap potentials including gravitational. For studies of their collective
Stability of Logarithmic Bose-Einstein Condensate in Harmonic Trap
In this paper we investigate the stability of a recently introduced Bose-Einstein condensate (BEC) which involves logarithmic interaction between atoms. The Gaussian variational approach is employed
Application of the theory of continuous media to the description of thermal excitations in superfluid helium
• Physics
• 2003
We propose a model for the quasiparticles of superfluid ${}^{4}\mathrm{He}$ which describes both phonons and rotons in a unified way. The theory is based on the fact that the thermal de Broglie
Velocity of Sound Density, and Gruneisen Constant in Liquid 4 He
• Physics
• 1970
By measuring the pressure dependence of the velocity of sound, we have determined both the pressure dependence of the density and the Gr\"uneisen constant $u$ of liquid $^{4}\mathrm{He}$.