Pulsed Nonlinear Sound in Superfluid 4He and 4He-3He Mixtures

Sound modes in ⁴ He and ⁴ He- ³ He mixtures which arise out of the two-fluid equations are made up up a vector convective flow and scalar temperature changes. A method for modeling nonlinear pulses of sound with geometric approximations to the vector and scalar components has recently been applied towards understanding nonlinear second sound near the lambda point. ⁶ The same method may be used, in general, for modeling linear and nonlinear sounds in Helium II. We demonstrate with a model for nonlinear second sound pulses in ³ He- ⁴ He mixtures and compare the results to experimental observations.     

Critical Supersaturation of Superfluid 3He-4He Mixtures

We report the results of our systematic study of the phase separation in supersaturated ³He-⁴He liquid mixtures of the ³He-dilute phase. The amount of the critical supersaturation is determined within the wide ranges of the temperature (0.4–645mK) and the pressure (1–8.5kgf/cm²). Using the data we construct the surface of critical supersaturation, x _3,cr (T,P), which enables us to recognize almost the overall behavior of the critical supersaturation in superfluid ³He-⁴He mixtures. The main specific features observed are (i) below 10mKx _{3, cr} is almost temperature-independent, (ii) above 10mK up to 500mKx _{3, cr} increases with the temperature, and (iii) above 500mKx _{3, cr} decreases smoothly with the increase of temperature down to zero at the tricritical point. We give various discussions from the viewpoint of the quantum nucleation, the classical thermal nucleation and the crossover between them.     

Effective Heat Conductivity and Relaxation Processes in Superfluid Mixtures of 3He-4He

The effective thermal conductivity coefficient'ceff in superfluid ³He-⁴He mixtures with concentration of 9.8% ³He has been studied experimentally between 100 and 500 mK, where the main contribution to the kinetic processes is made only by phonons and ³He impurity excitations. In this case the effective thermal conductivity is a combination of diffusivity, thermal conductivity and thermal diffusion. The κ _eff value was found from stationary measurements of the temperature gradients caused by the thermal flow and from the temperature relaxation kinetics. Both the methods provide consistent resugts which also agree with those on effective thermal conductivity calculated in terms of the kinetic theory of phonon-impuriton system.     

Second Sound Measurements Near the Tricritical Point in 3He-4He Mixtures

In this paper we discuss a pulsed second sound experiment, aimed at determining accurately the critical exponent , and the predicted logarithmic correction to scaling, for the superfluid density along a tricritical path in the ³ He- ⁴ He phase diagram. We present an accurate estimate for the limits for closest approach to the tricritical point, as set by gravitationally induced sample inhomogeneities and finite size effects, and discuss some of the complications associated with measurements close to the tricritical point.     

Acoustical Experiments on Superfluid 3He-4He Mixtures in Aerogel

This report discusses our results on the superfluidity of ³ He- ⁴ He mixtures in a 98% porosity silica aerogel. We have used low frequency sound to probe helium mixtures confined to aerogel, and have observed both the slow mode of superfluid ³ He in aerogel, which is manifested only below T_c, and an additional sound mode present only in the mixture. We attribute this novel sound mode to the slow-mode in the ⁴ He rich phase of the dilute ³ He- ⁴ He mixture. This mode exhibits positive frequency shifts below T_c in aerogel, while above T_c the mode is observed at a temperature independent frequency until close to T where it shifts to zero frequency.     

Critical Transport Properties Near the Superfluid Transition in 3He-4He Mixtures

The renormalization group(RG) functions for the critical dynamics at the λ-transition in ³He–⁴He mixtures (model F^′) have been calculated in two loop order. Comparison is made with the hydrodynamic transport coefficients as functions of the concentration of ³He. Improvement is achieved with respect to an earlier calculation based on a combination of one loop and two loop terms in the field theoretic functions, The non-universal initial values of the flow parameters take values more compatible with the physical expectation. As a corollary we obtain the field theoretic functions of model F describing the critical dynamics of the superfluid transition in pure ⁴He. Comparing with experiments in pure ⁴He improves the background value of the imaginary part of the time scale ratio between the order parameter and the entropy density.     

Diffusion and Thermal Diffusion Influence on Temperature Relaxation in Superfluid 3He-4He Mixtures

Formation of a nonequilibrium stationary state in quantum superfluid ³He-⁴He mixtures is studied in this paper. The problem is considered on a segment with the heat flow switched on at the left end and with the constant temperature at the right end. Second sound mode contribution and dissipative mode contribution is studied. The problem is solved at arbitrary temperatures and concentrations of ³He and this needs the accounting of diffusion and thermal diffusion processes in superfluid ³He-⁴He mixtures.     

Structure Factors of 3He-4He Mixtures

We briefly summarize the present understanding of the dynamic structure factors of liquid ³He-⁴He mixtures in the phonon-maxon-roton region and then present a new calculation using the memory function formalism. Results agree well with experimental data.     

Liquid-Vapor Coexistence in Two-Dimensional 3He-4He Mixtures

We present results from an ongoing study of the Liquid (L)-Vapor (V) coexistence boundary for single layer mixtures of ³ He and 4He adsorbed on two layers of H ₂ plating graphite. We are studying mixtures with ³ He molar fractions, x, of approximately 0.05, 0.1, 0.35, and 0.5, which we compare with previously published data for the pure isotopes. For the concentrations under study, we have approximate determinations of the L- V critical temperatures and of the low temperature density of the condensed phase.     

Second Sound Contribution to Temperature Gradient Evolution in Superfluid Mixtures

Starting from the full system of hydrodynamic equations for helium isotopic mixtures, the problem of temperature and concentration relaxation is solved. The limiting case of ultralow temperatures, when the contribution of thermal excitations can be neglected, is considered. A comparison with the experimental data is carried out.      

Nonlinear Second Sound Waves and Acoustic Turbulence in Superfluid 4He

The preliminary results of an investigation of nonlinear second sound waves in a high quality resonator filled with superfluid ⁴He are presented and discussed. It is found that, for a sufficiently strong periodic driving force, a cascade of second sound waves is formed at multiple harmonics of the driving frequency over the extremely wide frequency range 1–100 kHz. It can be described by a power law A _ω =const.×ω ^−m , where the scaling index m≈1. These observation can be attributed to the formation of a Kolmogorov-like turbulent cascade in the system of second sound waves, accompanied by directed energy flux through the frequency scales. It manifests itself as a limiting of the amplitude of a standing wave, a distortion of the shape of the initially harmonic waves, and a reduction of the effective quality factor Q of the resonator.     

Adiabatic Fountain Resonance for 4He and 3He-4He Mixtures

We report an analysis of a superfluid Helmholtz resonance in the case of helium confined in a superleak. The resonance of the superfluid is achieved under nearly adiabatic conditions. Equations are derived for the resonance frequency, the temperature oscillations of the superleak and the phase relation of this signal relative to an ac heat input. The resonance frequency yields the superfluid fraction of the confined helium. Data are analyzed as function of frequency and temperature and yield parameters such as the dissipation and thermal conductivity which determine the resonance line shape. Estimates are made of the thermodynamic parameters in the resonance equation by using derivatives along the pressure-temperature-concentration lambda surface. These parameters are compared with results from the analysis of the resonance.     

Fermi Liquid Properties of 3He-4He Mixtures

We calculate microscopically the spectrum of a ³ He impurity atom moving in ⁴ He, determine the Fermi-Liquid interaction between ³ He atoms and then calculate the pressure and concentration dependence of the effective mass and the magnetic susceptibility. The long wavelength limit of the spectrum defines the hydrodynamic effective mass. When k 1.7Å^–1 the motion of the impurity is damped due to the decay into a roton and a low energy impurity mode. The calculations of the Fermi-Liquid interaction are based on correlated basis functions (CBF); the relevant matrix elements are determined by the Fermi hypernetted-chain theory. Our theoretical effective masses agree well with recent measurements, ^1,2 but our analysis suggests a new extrapolation to the zero-concentration limit. With that effective mass we also find a good agreement with the measured ³ Landau parameter F ₀ ^a .     

Phonon-Impuriton Relaxation and Transport in 3He-4He Superfluid Solutions

No Heading The measurements of the effective thermal conductivity coefficient of a superfluid³He-⁴He mixture with initial concentration of 9.8% ³He are carried out in the temperature range 70 – 500 mK. The results obtained and the other experimental data available on effective thermal conductivity, shear viscosity, and spin diffusion are interpreted within the kinetic theory of phonon - impuriton system of superfluid solutions. It is shown that all experimental data can be explained by taking into account the following relaxation processes: longitudinal phonon relaxation, phonon scattering by impuriton, phonon absorption and emission by impuriton, and impuriton - impuriton interaction. The last process is characterized by different relaxation times for each transport phenomenon: transfer of mass, momentum, and nucleus spin. The impuriton - impuriton and phonon - impuriton relaxation times are estimated and the hierarchy of relaxation times in such system is established. The phonon longitudinal relaxation time in phonon diffusion process should be taken into account. The phonon and impuriton contributions to thermal conductivity, viscosity, and mass diffusion are estimated.PACS numbers: 66.20.+d, 67.60–g, 64.75+g, 67.40.Pm, 66.60+a, 66.30.Xj     

Possible Existence of Dense Superfluid 3He-4He Mixture in Aerogel

While studying superfluid ³He of 2.4 MPa in 97.5 %-porosity aerogel with NMR/MRI techniques, we find that the T _C is reduced when more than adequate amount of ⁴He, which covers the surface of silica strands, is introduced. For a sample, whose T _C is reduced to as low as 0.9 mK, we find that the spin diffusion coefficient in the normal phase is increased by a factor of 1.56 both in high temperature region, where ³He-³He scattering dominates, and in low temperature region, where ³He-aerogel scattering dominates. This enhancement is attributed to a modification of Landau parameter $F_{0}^{a}$ from ?0.757 to ?0.62, which is a change towards less ferromagnetic direction. The modification of microscopic quantity could be explained if small amount of ⁴He has homogeneously mixed into liquid ³He in the aerogel.     

3He-4He Mixtures in 95% Porous Aerogel

Torsional oscillator measurements of ³ He- ⁴ He mixtures in 95% porous aerogel found a phase diagram similar to that in 98% porous aerogel. The coexistence boundary on the ³ He rich side resides very close to, but nevertheless is detached from the superfluid transition line. Together with the findings in 98%, 87%, and 99.5% porous aerogel, this result supports the interpretation that the phase separation of ³ He- ⁴ He mixture in aerogel is induced by the capillary condensation of ⁴ He films from neighboring silica strands into ⁴ He rich domains.     

Spin-Spin Relaxation in Phase-Separated 3He-4He Solid Mixtures

The spin-spin relaxation time T ₂ in a ³ He- ⁴ He solid mixture with an initial concentration of 3.18% ³ He is measured during its phase separation in a temperature range of 1-250 mK. Cooling down to the region of separation was carried out by small steps (10 mK) followed by temperature stabilization for many hours. The time T ₂ was measured by using the pulsed NMR technique at a frequency of 250 kHz. The spin echo method makes it possible to distinguish the contributions to magnetic relaxation from both the concentrated and the dilute separated phases. The relaxation time T ₂ in the concentrated phase is found to be practically independent of temperature down to 50 mK and is determined by the same ³ He- ³ He exchange interaction as in pure bulk solid ³ He. It is found that the behavior of the spin echo signal at ultralow temperatures exhibits an anomaly, which may be connected with quasi-one-dimensional spin diffusion. In the dilute daughter phase the spin-spin relaxation time is inversely proportional to concentration and is described correctly by the Torrey model taping into account ³ He- ⁴ He tunnel exchange. The values of T ₂ in this phase coincide with those for a homogeneous (non-separated) mixture of the same concentration.     

Nuclear Magnetism of Normal 3He and 3He-4He Mixtures in Aerogel

We report NMR experiments at 8 T on ³ He and ³ He- ⁴ He mixtures filling the pores of 95% porous aerogel, for temperatures T 6 mK. Magnetization measurements of pure ³ He reveal a localized layer approximately one monolayer thick. The longitudinal relaxation includes a component logarithmic in time, which is apparently associated with a fraction of the localized ³ He atoms. When the localized ³ He is displaced by adding ⁴ He the logarithmic relaxation disappears and T ₁ for the dominant exponential relaxation increases. Measurements of the spin diffusion coefficient with the aerogel filled with dilute solution in equilibrium with bulk phase-separated mixture provide an unambiguous determination of the spin mean free path,_s = 58 nm     

Dissipation in Superfluid 3He Weak Links

We suggest a new interpretation of the Berkeley data on the dissipation of superflow in Josephson junctions in superfluid ³He-B. The measurements are well described by the following relation between the current through a junction and the pressure head applied to it (current-pressure relation or CPR): $I = G_1 P + G_2 \sqrt P $ . The Berkeley group has proposed an explanation based on 1) ballistic removal of quasiparticles from the junction; 2) dissipative motion of the anisotropy axis of the order parameter inside the junction. We argue that part 1) of the model, which is responsible for the G ₂ part of the CPR, is invalid, since it presumes the existence, in the bulk, of quasiparticles with energies inside the superfluid gap. Part 2) which is responsible for the G ₁ term implies that the anisotropy axis of the order parameter strongly depends on the phase difference across the junction. Our agternative model is based on mechanisms well known in superconductors: dissipation due to time lag of inequilibrium order parameter and/or Andreev reflection of quasiparticles trapped inside the junction. For the parameters of the Berkeley experiment these models give the same order of magnitude for the G ₁ in the CPR, and are in rough agreement with the experiment. The nature of the G ₂ term remains mysterious. It could arise due to saturation of the current of Andreev-scattered quasiparticles if the quasiparticle relaxation time in the junction is considerably longer than in normal Fermi liquid.     

Phase Separation Kinetics of Solid 3He-4He Mixtures

The kinetics of isotopic phase separation in solid mixture of ³ He in ⁴ He with the initial concentration 2.05 % at various molar volumes has been investigated by precise pressure measurements. It has been shown that during both stepped and fast cooldown into the metastable region the equilibrium of coexisting phases is described by the exponential law with a characteristic time constant , The value of is found to decrease as the molar volume increases and the temperature lowers. It confirms that the growth of the ³ He-rich phase is connected with nonthermally activated (quantum) diffusion in the gas of delocalized ³ He quasiparticles. The obtained experimental results can be described only qualitatively by current kinetic theory of binary quantum solid mixtures. The conditions permitting the realization of the isotopic phase separation during the time observed in the experiment are analyzed. The effective quantum diffusion coefficient providing required ³ He atoms transport is about an order of magnitude higher than the corresponding value measured in NMR experiments. These conditions are probably fulfilled at the big concentration gradient which takes place at isotopic phase separation. The corresponding kinetic theory should be developed.