Sound and dissipation coefficients in the phonon-impurity system of 3He-4He solutions

Abstract

The phonon-impurity system of dilute solutions of 3He in 4He is studied experimentally and theoretically using an acoustic technique. The sound velocity and absorption measurements make it possible to identify the theoretically predicted new mechanism of phonon relaxation with anomalous dispersion in the presence of impurities. A kinetic problem for arbitrary frequencies is solved, which also enables us to obtain all the dissipation coefficients of the solutions and to explain the experimental data on second-sound absorption, thermal conductivity, and heat pulse propagation. The relation is considered between relaxation processes in a phonon-impurity system and the phonon spectrum dispersion in 3He-4He solutions.

Relaxation time hierarchy in a two-component quasiparticle gas

“…However, by projecting on the nucleus of an integral operator of collisions it is possible to define somewhat inverse matrix. In the present work this procedure has been made with the help of introducing of projection operator (22) corresponding to conservation of total momentum of a quasiparticle system. As an outcome it allowed me to obtain the general expression (29) for characteristic time (see also eq.…”

“…If C jk depends on momenta, then speed of equilibration of a system depends on how fast the equilibration between identical quasiparticles is 15,19 . Such situation brightly manifests in a phonon-impuriton system of superfluid mixtures of helium isotopes 22 and in phonon systems in solids 16 . There is a two-stage mechanism of relaxation in these systems.…”

Chapter 3: Thermodynamics and Hydrodynamics of 3He-4He Mixtures

“…Adamenko and Rudavskii (1987) have reviewed the kinetics of the phonon-impurity system of 3He-4He superfluid solutions. Work regarding the various types of sounds is reported by Fujii et al (1986), Lea et al (1987), Wiegers et al (1988), and Adamenko et al (1988). Recent papers on thermal convection are written by Fetter (1982), Ecke et al (1987), Bloodworth et al (1987), .…”

Kinetic theory of first sound in He II and 3He-4He superfluid mixtures

“…To find the coefficient of sound attenuation oq it is necessary to calculate matrix element (32). From relations (23) …”

“…In our calculations we assume that time -7"33 is pressure independent, as it follows from the experimental data; and that the times of phonon-impuriton and phononroton interactions change with the rise of pressure due to the pressure dependence of all parameters that determine 36 ~'li~-As for the phonon spectrum at high pressure we use the expressions proposed in Ref. 34. Note that the roton energy gap decreases when the pressure increases and this Causes the rise of the roton contribution to sound attenuation at T> 0.5 K.…”