Superfluid Transition Of 4He Research Articles

Linear and nonlinear heat transport near the superfluid transition of4He

A brief summary of the present status of the renormalization-group theory of heat transport near the superfluid transition of4He is presented. This includes the thermal conductivity, second-sound damping, mutual friction coefficients, boundary resistance and nonlinear effects on the temperature profile in the presence of a finite heat current.

Thermal expansion coefficient near the superfluid transition of 4He in an aerogel.

We measured the isobaric thermal expansion coefficient {beta}{sub {ital P}} near the superfluid transition of {sup 4}He in an aerogel along six isobars between 3 and 24 bars. The data yield the specific-heat exponents {alpha} and {alpha}{prime} and amplitude ratio {ital A}/{ital A}{prime}. Fits by power laws in {ital t}{equivalent to}{ital T}/{ital T}{sub {ital c}}{minus}1, where {ital T}{sub {ital c}} is the transition temperature, produced {alpha}{congruent}{minus}0.6 and {alpha}{prime}{congruent}{minus}1.0{ne}{alpha}. Including an analytic background {ital a}{times}{ital t} permitted {alpha}={alpha}{prime}{congruent}{minus}0.59, but required a very large coefficient {ital a} and yielded {ital A}{prime}/{ital A}{congruent}0. The exponents are inconsistent with that of {rho}{sub {ital s}} and hyperscaling in three dimensions.

Nonlinear heat transport near the superfluid transition of 4He.

We investigate the effect of a finite heat current Q on the superfluid transition of $^{4}\mathrm{He}$. We perform a renormalization-group (RG) calculation of the temperature profile and of the critical thermal conductivity ${\ensuremath{\lambda}}_{\mathit{T}}$(Q) in the nonlinear-response regime. In the experimentally accessible region close to ${\mathit{T}}_{\ensuremath{\lambda}}$ we predict the divergence ${\ensuremath{\lambda}}_{\mathit{T}}$(Q)\ensuremath{\sim}${\mathit{Q}}_{\ensuremath{\lambda}}^{\mathrm{\ensuremath{-}}\mathit{y}}$ with the effective exponent ${\mathit{y}}_{\ensuremath{\lambda}}$\ensuremath{\approxeq}0.31. An experiment is proposed to detect this nonlinear effect. We also present the exact RG result x=(2\ensuremath{\nu}${)}^{\mathrm{\ensuremath{-}}1}$ for the depression of the transition temperature ${\mathit{T}}_{\ensuremath{\lambda}}$-${\mathit{T}}_{\ensuremath{\lambda}}$(Q)\ensuremath{\sim}${\mathit{Q}}^{\mathit{x}}$.

Some aspects of the effect of gravity on the superfluid transition in4He

After a brief review of the experimental study of the effect of gravity on the superfluid transition, various options are discussed for choosing a reference superfluid-transition temperature for a sample in the presence of gravity where there is no unique transition. Thereafter some presently feasible experiments are discussed, which could be substantially improved in a microgravity environment.

Measurements of the superfluid transition in helium by means of a vibrating reed

A relatively simple method is presented that has been used in an undergraduate experimental course for observing the superfluid transition in 4He. The experimental technique consists of submerging a vibrating reed in liquid helium and observing the changes in frequency and damping (energy dissipation) as the temperature is regulated above and below the superfluid transition. The results of the measurements are interpreted by means of a simplification of the acting hydrodynamic forces, and it is seen that most of the relevant physics is well described by the approximations.

Superfluid transition of 4He in aerogel

The superfluid transition of 4 He in some porous media is studied through a fractal model. We incorporate the fractal aspects of the medium in both the Harris criterion and the hyperscaling relations, so that the experimentally observed non-bulk exponents can be consistently explained as resulting from a crossover to new behavior. Available data for aerogel suggest that the superfluid transition in this case is a fractal surface (as opposed to volume phenomenon, which can be modelled microscopically by means of an inhomogeneous effective mass.

Superfluid transition of 4He in aerogels

Superfluid transition of 4He in aerogels

On the Superfluid Transition of 4He in Restricted Geometries: A Model for 4He in Zeolite

On the Superfluid Transition of 4He in Restricted Geometries: A Model for 4He in Zeolite

Transport properties of helium near the liquid-vapor critical point. IV. The shear viscosity of3He and4He

Shear viscosity measurements with a precision of 0.05% are reported for3He and4He along near-critical isochores 0.85<ρ/ρc<1.12, where ρc is the critical density. The temperature range was −10−4<e<1, where e=(T − Tc)/Tc is the reduced temperature. The experiments were carried out with a torsional oscillator operating at 158 Hz, driven at resonance in a phase-locked loop. The absolute value of the viscosity was obtained by calibration at the superfluid transition of4He, based on published values and from direct calculations using the free decay time constant of the oscillations. The data are analyzed in terms of a model using the recent mode-coupling (MC) expressions by Olchowy and Sengers, and where account is taken of the earth's gravity effects. The theory could be fitted very well to the experiment with a single free parameter, the cutoff wave numberqD, which was found to be 3.0×106 and 7.0×106 cm−1 for3He and4He, respectively. We have used for the critical exponent the MC predicted value of zη=0.054, which permits a fit superior to that using zη=0.064 predicted by dynamic renormalization group (DRG) theories. Detailed comparisons are made between the model calculations and data for various isochores and isotherms and good agreement is obtained. The effects of gravity are described in some detail. The predicted frequency effect in viscosity measurements is calculated for3He and is shown to be obscured by gravity effects. Using the Olchowy-Sengers formulas, we have also fitted the MC theory to the critical thermal conductivity data of3He, again withqD as the only free parameter. This fit gaveqD=6 × 107 cm−1, which in the ideal situation should have been the same asqD from viscosity. We also discuss a representation of the3He viscosity data along the critical isochore by a power law and first correction-to-scaling erm. Using the viscosity and the critical conductivity data for3He, we have calculated the dynamic amplitude ratio and obtained ℛ=1.05±0.10, in agreement with predictions from MC and DRG theories. Also, ℛ agrees with data of classical fluids. Finally, a comparison is made of recent shear viscosity data for CO2 by Bruschi and Torzo with those on He. The CO2 data are also analyzed in terms of the MC theory, and the discrepancies are discussed. In the Appendices, we present the results of new compressibility measurements on3He along the critical isochore, as used in the MC analysis. We also present a brief analysis of the fluid hydrodynamics in the torsional oscillator leading to relations for the viscosity as a function of the measured quantities. Finally, we give a short outline of the vertical density profile calculations from the earth's gravity field for the calculations of the viscosity nearTc.

Technique for determining second-sound attenuation near the superfluid transition in 4He

A procedure has been developed to measure the attenuation of second sound in liquid helium at temperatures near Tλ. The decay rate of a second-sound resonance in a high-Q cavity is determined, and data for more than one harmonic is obtained allowing the separation of the attenuation due to bulk fluid from losses at the cavity walls. This method has proven particularly successful near Tλ, where the second-sound velocity is strongly dependent on temperature and a high degree of temperature stability is needed. Results are given for the temperature range 40 μK&amp;lt;Tλ-T&amp;lt;40 mK at saturated vapor pressure. With minor modifications the apparatus can be used for measurements at elevated pressure and over a much wider range of temperatures.

Superfluid transition of4He films adsorbed on graphite substrates: A calorimetric study in connection with third-sound observations

The heat capacity of4He films adsorbed on Grafoil has been reexamined with emphasis on its correlation with our previous third-sound observations. Each of the heat capacity curves shows an inflection point, which shifts to lower temperature as the film gets thinner. The temperature of this inflection point is higher than the onset temperature determined by the third-sound measurements for any given thickness. This result can be explained within the framework of recent theoretical studies based on the Kosterlitz-Thouless theory. In addition, the van der Waals constant α is evaluated from the data on vapor pressure versus temperature, and it is estimated to be 201±30 me V A3 (=50.1±7.5 K layer3) in good agreement with a recent theoretical value derived by Vidali et al. Moreover, this evaluation confirms our previous conclusion deduced from third-sound observations.

Nonlinear renormalization-group analysis applied to the hydrodynamic light scattering spectrum of4He belowT ?

We calculate the observable critical temperature dependence of the transport coefficients entering the hydrodynamic form of the dynamic structure factor of4He belowTλ. Application of our recently introduced nonlinear renormalization-group analysis yields quantitative agreement with previous light scattering experiments in the hydrodynamic region. This resolves a long-standing problem in the critical dynamics below the superfluid transition of4He.

Nonasymptotic critical dynamics near the superfluid transition in4He

We study the crossover regime between the asymptotic critical dynamics and the noncritical background behavior near the superfluid transition of4He. We demonstrate in quantitative detail that our recently introduced nonlinear dynamic renormalizationgroup treatment is indispensable for an appropriate description of the observable critical dynamics. The global features of the flow diagram in the dynamic parameter space of the symmetric planar-spin model of Halperin, Hohenberg and Siggia are discussed. The range of applicability of various local approximations is investigated. The theory is applied to explain the thermal conductivity data of Ahlers in the range 10−6<t<10−2 of relative temperaturet=(T−Tλ)/Tλ. Special attention is paid to the dependence on the value of the borderline dimensiond* where dynamic scaling breaks down. Excellent agreement with experiment is found only ford*≈3 which is consistent with recent theoretical estimates ofd*. The theory matches well also with the noncritical background behavior. Predictions are made for the range 10−9<t<10−6.

The dielectric constant in liquid and solid4He

We report precision measurements of the dielectric constant e of liquid and solid 4 He at constant density as a function of temperature in the range0.1<T<1.2 K. For these measurements a capacitance bridge was used, the stability of which permitted a reproducibility of δe / e ≈ 6×10−9 in the dielectric constant. We find that the polarizabilityp, defined by the Clausius-Mosotti equation, is a weak function of temperature. This dependence onT at the low-temperature end diminishes as the density of 4 He is decreased to that at saturated vapor pressure. We also describe briefly attempts at measuring the change of e at the superfluid transition in 4 He and during the melting process, all corrected to conditions of constant volume, and upper limits for these changes are given. Finally, we present measurements of e in liquid 4 He at saturated vapor pressure between 0.15 and 1.3 K, from which we deduce the change in density. The results are compared with recent data obtained with a microwave cavity method and good agreement is found. Further comparisons are made with Van Degrift's results at 4 MHz and also with other recent data above 0.7 K.