Temperature, pressure, and concentration dependence of the thermal conductivity of very dilute solutions of3He in superfluid4He

Rosenbaum, Ralph; Landau, J.; Eckstein, Y.

doi:10.1007/bf00655864

Cited by 70 publications

(45 citation statements)

References 15 publications

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“…3 the various scattering rates in the problem. Whereas the 3 He-3 He scattering rate is much larger than the 3 He-phonon rate at the high concentrations of the Lamoreaux, et al [4] and Rosenbaum, et al [7] measurements, at x 3 ∼ 10 −6 , they are roughly equal, and at lower concentrations, the scattering of 3 He by phonons (or walls, depending on the geometry [12]) dominates. In treating phonon-phonon scattering we use the fact that phonons propagating in a given direction in momentum are in local equilibrium, owing to the very large small angle scattering rate.…”

Section: Discussionmentioning

confidence: 99%

“…For the high 3 He concentrations of Refs. [4,7], where 3 He-3 He scattering keeps the 3 He in equilibribum, we can ignore the energy transfer relative to the momentum transfer, k, in the 3 Hephonon scattering. However, in general, it is necessary to consider both.…”

Section: Discussionmentioning

confidence: 99%

“…In this paper, starting from microscopic scattering processes we calculate transport coefficients of dilute solutions in the regime where phonons dominate the 4 He excitations and the 3 He concentrations are low enough for classical statistics to be valid. This regime encompasses the range at relatively high 3 He concentrations where measurements have been carried out [4,7], to the range of natural concentration, x 3 ∼ 10 −6 where future measurements are being prepared [8], to the low concentrations anticipated in the Oak Ridge neutron electric dipole moment experiment [3]. Our primary focus here is on the processes of thermal conduction and diffusion.…”

Section: Introductionmentioning

confidence: 99%

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Low-Temperature Transport Properties of Very Dilute Classical Solutions of $$^3$$ 3 He in Superfluid $$^4$$ 4 He

2014

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We report microscopic calculations of the thermal conductivity, diffusion constant and thermal diffusion constant for classical solutions of 3 He in superfluid 4 He at temperatures T < ∼ 0.6 K, where phonons are the dominant excitations of the 4 He. We focus on solutions with 3 He concentrations < ∼ 10 −3 , for which the main scattering mechanisms are phonon-phonon scattering via 3-phonon Landau and Beliaev processes, which maintain the phonons in a drifting equilibrium distribution, and the slower process of 3 He-phonon scattering, which is crucial for determining the 3 He distribution function in transport. We use the fact that the relative changes in the energy and momentum of a 3 He atom in a collision with a phonon are small to derive a Fokker-Planck equation for the 3 He distribution function, which we show has an analytical solution in terms of Sonine polynomials. We also calculate the corrections to the Fokker-Planck results for the transport coefficients.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Low-Temperature Transport Properties of Very Dilute Classical Solutions of $$^3$$ 3 He in Superfluid $$^4$$ 4 He

2014

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“…24 and 27, can be considered as rll--~2.6X 10-1~ -5 (11) Such an approximation for 144 is permissible at x3> 10 -4, since in the previously described solutions, as will be shown below, the establishment of complete equilibrium in the phonon system is governed by the phononimpurity collisions, rather than by the phonon-phonon transverse relaxation.…”

Section: Collision Integralsmentioning

confidence: 99%

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

et al. 1988

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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.

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“…3 These works are based on phonon-3He interactions which are characterized by two processes: elastic phonon scattering with 3He and phonon absorption by 3He.l Rosenbaum et al 4 measured the thermal conductivity, and Kuenhold et al 5 performed an experiment for the viscosity of dilute 3He-4He mixtures. 3 These works are based on phonon-3He interactions which are characterized by two processes: elastic phonon scattering with 3He and phonon absorption by 3He.l Rosenbaum et al 4 measured the thermal conductivity, and Kuenhold et al 5 performed an experiment for the viscosity of dilute 3He-4He mixtures.…”

Section: Introductionmentioning

confidence: 99%

Thermal conductivity and viscosity in dilute3He−4He mixtures below 0.6 K

Lee

Yoo

et al. 1997

J Low Temp Phys

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The effects of three-phonon processes on the phonon thermal conductivity and phonon viscosity in dihtte JHe-"He mixtures below 0.6 K are investigated. The characteristic scattering times for phonon-phonon interaction-limited thermal con&tctivity and viscosity are calculated from a collision matrix which contains information on the three-phonon processes. We find that due to phonon-~He interactions the phonon momentum range in which threephonon processes occur is reduced in comparison with that of the pure 4He case. Results for thermal conductivity and viscosity show good agreement with experimental data without having to adjust the rates of phonon absorption by 3He and the rates of elastic scattering of phonons with SHe. 495 0022-2291/97/I 100-0495512.50/0 g!! I997 Plenum Publishing Corporation 496 C.-i. Um et aL

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Temperature, pressure, and concentration dependence of the thermal conductivity of very dilute solutions of3He in superfluid4He

Cited by 70 publications

References 15 publications

Low-Temperature Transport Properties of Very Dilute Classical Solutions of $$^3$$ 3 He in Superfluid $$^4$$ 4 He

Low-Temperature Transport Properties of Very Dilute Classical Solutions of $$^3$$ 3 He in Superfluid $$^4$$ 4 He

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

Thermal conductivity and viscosity in dilute3He−4He mixtures below 0.6 K

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