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

Baym, Gordon; Beck, D.; Pethick, C. J.

doi:10.1007/s10909-014-1235-0

Cited by 10 publications

(22 citation statements)

References 15 publications

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“…[2]), first for the phonons. The momentum-dependent mean free path of a phonon of momentum q scattering against the 3 He,…”

Section: Phonon and 3 He Relaxationmentioning

confidence: 99%

“…is typically greater than 1 km for x 3 < ∼ 10 −9 and T ∼ 0.5 K [2]; here γ q is the corresponding scattering rate, s is the phonon velocity, and J is an angle-integrated rate constant. Therefore, phonon-wall and phonon-phonon scatterings determine the phonon distribution.…”

Section: Phonon and 3 He Relaxationmentioning

confidence: 99%

“…As discussed in Refs. [2] and [9], rapid, small angle phononphonon scattering establishes thermal equilibrium along phonon 'rays,' i.e., given directions in momentum space, with the distribution…”

Section: Phonon and 3 He Relaxationmentioning

confidence: 99%

“…Here we extend the solution of the Boltzmann equations in Ref. [2] to include these effects, in addition to providing some examples for x 3 < ∼ 10 −9 . For illustration, we consider the effect of a heat current in an essentially one dimensional geometry, with the 3 He superfluid 4 He mixture in a long pipe with a diameter of a few cm.…”

Section: Introductionmentioning

confidence: 98%

“…For concentrations x 3 > ∼ 10 −4 , the reverse situation holds: the 3 He are in local equilibrium due to rapid 3 He-3 He scattering and the phonon distribution is distorted due to phonon-3 He interactions [1]. In the intermediate concentration regime, the phonon and 3 He distributions are both distorted and must be determined by solving the coupled evolution, or Boltzmann, equations [2]. At the highest concentrations, x 3 ∼ 1%, Fermi-Dirac statistics for the 3 He become important [3].…”

Section: Introductionmentioning

confidence: 99%

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Transport in ultradilute solutions ofHe3in superfluidHe4

2015

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We calculate the effect of a heat current on transporting 3 He dissolved in superfluid 4 He at ultralow concentration, as will be utilized in a proposed experimental search for the electric dipole moment of the neutron (nEDM). In this experiment, a phonon wind will generated to drive (partly depolarized) 3 He down a long pipe. In the regime of 3 He concentrations < ∼ 10 −9 and temperatures ∼ 0.5 K, the phonons comprising the heat current are kept in a flowing local equilibrium by small angle phononphonon scattering, while they transfer momentum to the walls via the 4 He first viscosity. On the other hand, the phonon wind drives the 3 He out of local equilibrium via phonon-3 He scattering. For temperatures below 0.5 K, both the phonon and 3 He mean free paths can reach the centimeter scale, and we calculate the effects on the transport coefficients. We derive the relevant transport coefficients, the phonon thermal conductivity and the 3 He diffusion constants from the Boltzmann equation. We calculate the effect of scattering from the walls of the pipe and show that it may be characterized by the average distance from points inside the pipe to the walls. The temporal evolution of the spatial distribution of the 3 He atoms is determined by the time dependent 3 He diffusion equation, which describes the competition between advection by the phonon wind and 3 He diffusion. As a consequence of the thermal diffusivity being small compared with the 3 He diffusivity, the scale height of the final 3 He distribution is much smaller than that of the temperature gradient. We present exact solutions of the time dependent temperature and 3 He distributions in terms of a complete set of normal modes.

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“…[2]), first for the phonons. The momentum-dependent mean free path of a phonon of momentum q scattering against the 3 He,…”

Section: Phonon and 3 He Relaxationmentioning

confidence: 99%

Section: Phonon and 3 He Relaxationmentioning

confidence: 99%

Section: Phonon and 3 He Relaxationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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Transport in ultradilute solutions ofHe3in superfluidHe4

2015

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On the Transition from Potential Flow to Turbulence Around a Microsphere Oscillating in Superfluid $$^4\hbox {He}$$ 4 He

2017

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The flow of superfluid 4 He around a translationally oscillating sphere, levitating without mechanical support, can either be laminar or turbulent, depending on the velocity amplitude. Below a critical velocity vc that scales as ω 1/2 , and is temperature independent below 1 K, the flow is laminar (potential flow). Below 0.5 K the linear drag force is caused by ballistic phonon scattering that vanishes as T 4 until background damping, measured in the empty cell, becomes dominant for T < 0.1 K. Increasing the velocity amplitude above vc leads to a transition from potential flow to turbulence, where the large turbulent drag force varies as (v 2 − v 2 c ). In a small velocity interval ∆v/vc ≤ 3% above vc, the flow is unstable below 0.5 K, switching intermittently between both patterns. From time series recorded at constant temperature and driving force, the lifetimes of both phases are analyzed statistically. We observe metastable states of potential flow which, after a mean lifetime of 25 minutes, ultimately break down due to vorticity created by natural background radioactivity. The lifetimes of the turbulent phases have an exponential distribution, and the mean increases exponentially with ∆v 2 . We investigate the frequency at which the vortex rings are shed from the sphere. Our results are compared with recent data of other authors on vortex shedding by moving a laser beam through a Bose-Einstein condensate. Finally, we show that our observed transition to turbulence belongs to the class of "supertransient chaos" where lifetimes of the turbulent states increase faster than exponentially. Peculiar results obtained in dilute 3 He -4 He mixtures are presented in the Appendix.

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Excitations in the quantum liquid⁴He: A review

Glyde

2017

Rep. Prog. Phys.

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Progress made in measuring and interpreting the elementary excitations of superfluid and normal liquid \4he in the past 25 years is reviewed. The goal is to bring up to date the data, calculations and our understanding of the excitations since the books and reviews of the early 1990s. Only bulk liquid \4he is considered. Reference to liquid \3he, mixtures, reduced dimensions (films and confined helium) is made where useful to enhance interpretation. The focus is on the excitations as measured by inelastic neutron scattering methods. The review covers the dynamic response of liquid \4he from the collective excitations at low energy and long wavelength (i.e. phonon-roton modes) to the single particle excitations at high energy from which the atomic momentum distribution and Bose-Einstein condensate fraction are determined. A goal is to show the interplay of these excitations with other spectacular properties such as superfluidity and the test of fundamental calculations of quantum liquids that is possible. The role of Bose-Einstein condensation in determining the nature of the \pr~ mode and particularly it's temperature dependence is emphasized. The similarity of normal liquid \4he with other quantum and classical liquids is discussed. .

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

Cited by 10 publications

References 15 publications

Transport in ultradilute solutions ofHe3in superfluidHe4

Transport in ultradilute solutions ofHe3in superfluidHe4

On the Transition from Potential Flow to Turbulence Around a Microsphere Oscillating in Superfluid $$^4\hbox {He}$$ 4 He

Excitations in the quantum liquid⁴He: A review

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

Cited by 10 publications

References 15 publications

Transport in ultradilute solutions ofHe3in superfluidHe4

Transport in ultradilute solutions ofHe3in superfluidHe4

On the Transition from Potential Flow to Turbulence Around a Microsphere Oscillating in Superfluid $$^4\hbox {He}$$ 4 He

Excitations in the quantum liquid4He: A review

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Excitations in the quantum liquid⁴He: A review