Path Integral Calculation of 4He in?Quasi-one-dimensional Channels

We consider ⁴He particles confined in a quasi-one-dimensional nanoscale channel in the range of liquid density, and numerically calculate the energy per particle by the imaginary time path integral Monte Carlo method. When the channel diameter becomes less than 1.6 nm, T _onset, at which the energy drops due to the particle exchange effect, shifts to lower temperature, and disappears below 0.48 nm. The diameter dependence of T _onset is similar to the behavior of the superfluid onset temperature, T _o, for mesoporous materials FSM16 observed by the torsional oscillator.     

Can Superfluid Vortex Lines Excite Normal Fluid Turbulence in 4He?

When helium II is made turbulent the superfluid component forms a dense tangle of quantized vortex lines which can be easily detected experimentally using the second sound technique. On the contrary little is known about the normal fluid component: on the experimental side progress has been hindered by the lack of simple flow visualization, and on the theoretical side attention has been concentrated on the effect that a given normal flow has on the superfluid vortices, not vice-versa. Attempting to fill this gap, we discuss results of recent calculations in which we find that normal fluid vorticity structures can be generated by superfluid vortices. In particular we address the issue of whether the superfluid vortices can make the normal fluid turbulent.     

3He Effect on 2D Superfluidity in 3He–4He Mixture Films on Planar Gold

There have been a number of experiments exploring the nature of 2D superfluidity and the configuration of ³He–⁴He mixture films on various substrates. To date, a possible film-structure at T=0 is that of a simple layer model, ³He/superfluid ⁴He/solid-like ⁴He/substrate, in which the submonolayer superfluidity is strongly affected by the coverage of the ³He overlayer. Yet the mechanism is not been fully understood. In this paper, we report a QCM study at 60 MHz for the ³He effect on the superfluidity of mixture films on flat gold, mainly focusing on the anomalous depletion of the temperature dependence of the superfluid density σ _s. In the measurements, we kept the ³He coverage constant (n ₃= 0, 3.6, 7.2, 19.0, 57.2, or 92.8 μmol/m²) and then incrementally added ⁴He. We observed the evolution of the ³He effect on σ _s(T) with increasing ³He coverage; this depletion of σ _s(T) rapidly increases and then saturates near n ₃～1 layer. From the analysis of the linear-temperature region in the plot of the dissipation peak temperature T _p as a function of the superfluid ⁴He coverage n _4s and comparison with previous studies on Mylar and porous gold, we found a universal function for the strength of the ³He effect for all substrates.     

Transport in 3He–4He Mixtures in Restricted Geometry

The effect of wall scattering on transport in dilute degenerate ³He–⁴He mixtures in quasi-2D flow channels or films is discussed. The calculation of the quasiparticle mean free path combines particle–wall and particle–particle collisions including the interference between them. The spin polarization affects the wall-driven contribution by changing bulk mean free path and particle wavelength. The expressions for the wall contribution to transport coefficients are especially transparent in the limiting cases of large and small bulk mean free paths. The calculated temperature, concentration, and polarization dependences of the transport coefficients allow one to extract parameters of surface roughness from experimental data on transport.     

Does the Kibble Mechanism Operate in Liquid 4He?

A rapid passage of liquid ⁴He through the lambda (superfluid) transition is expected (W. H. Zurek, Nature 317, 505; 1985) to result in the production of topological defects (quantized vortices) through the Kibble mechanism, the same process that is believed to have produced cosmic strings at the GUT phase transition of the early universe. But recent experiments (Dodd et al, Phys. Rev. Lett 81, 3703; 1998)) show that the density of vortices created, if any, seems to be smaller than predicted by a factor of at least 100. Possible ways of improving the sensitivity of the experiment are discussed.     

Recent Progress in Thin 3He–4He Films

We review recent work on the properties of ³He–⁴He thin film mixtures. The subject is introduced by reviewing the contributions made by Gasparini and co-workers. In the first part of this survey, we examine a microscopic calculation of the effects that an adsorbed ³He component has on the collective excitations associated with a ⁴He film, third sound. The work in question computes the change in the third sound velocity due to adding ³He, and we can compare this with existing experiment. For small ³He coverage, the change in the third sound speed depends on the derivatives of the species chemical potentials with respect to the areal density. The microscopic calculation shows oscillations in the third sound speed that reflect the layered structure of the film. In the second part of this survey, we concentrate on the ³He component. An important impact of the ⁴He environment is to change the bare mass in the limit of zero ³He concentration to a hydrodynamic mass. Quasiparticle interactions are introduced through the Landau parameters. Our Landau parameters are determined by fitting s-wave and p-wave T-matrix components using experimental results for the effective mass and the spin susceptibility. We can then predict the thermodynamic behavior of the mixture films at finite polarization, and in addition we can predict the spectrum of zero-sound excitations at all polarizations.     

Experiments on 3He–4He Mixtures in Aerogel

We describe experiments on ³ He- ⁴ He mixtures in 98% open aerogel grown by cold-deposition (T80mK) of ⁴ He followed by the deposition of ³ He or alternatively by cooling down a homogenous mixture. The two approaches led to different ⁴ He film morphologies. We will also describe the observation of migration of ⁴ He from or toward the cell below 100 mK. This migration can lead to the exclusion of ⁴ He (other than the localized surface layers) for ⁴ He concentrations between 4% and 11% in the cell.     

On Flow of He II in Channels with Ends Blocked by Superleaks

We report an experimental investigation of a flow of the superfluid phase of ⁴He–He II—thermally induced by a fountain pump through vertical channels of square cross-section with ends blocked by sintered silver superleaks and its decay. We confirm the existence of a weakly temperature dependent critical velocity v _cr ^I of order 1 cm/s, which does not scale with the channel size and is therefore an intrinsic property of the self-sustained vortex tangle of vortex line density L, measured by second sound attenuation. In addition to the previously reported turbulent A-state characterized by L ^1/2=γ(T)(v?v _cr ^I ), where v is the mean superflow velocity through the channel, we have discovered a new B-state characterized by L=β(v?v _cr ^II ), where β seems only weakly temperature dependent. It poses an important question why, at higher flow velocities, the quadratic generation mechanism, so well established in thermal counterflow, ceases to work. We offer a phenomenological model assuming that in the B-state the coarse-grained superflow profile matches the classical parabolic profile, with a finite, temperature dependent slip velocity v _cr ^II of order few cm/s and that a confined viscous normal fluid flow of toroidal form is induced inside the channel due to the mutual friction force. When the fountain pump is switched off, after an initial decay, a confined quasi-viscous flow of a single-component fluid with an effective kinematic viscosity ν _eff(T) establishes, giving rise to the observed exponential decay. The values of ν _eff(T), calculated using our model from the measured decay times, are in agreement with those deduced from other experiments on decaying He II turbulence.     

Theoretical Study of Quantum Gel Formation in?Superfluid 4He

Bosonic density functional theory calculations were carried out for neon, argon, and fluorine based systems in superfluid ⁴He with an emphasis on the formation of dimeric species in the liquid. These atomic species display relatively strong binding with helium and hence their solvation structures in the liquid exhibit highly localized liquid helium layers around them. These solvent layers modify the gas phase dimer potentials by inclusion of a recombination barrier, which provides stabilization for the solvated atoms. Of closed shell species neon is shown to exhibit a recombination barrier of 3 K for the dimer and up to 5.8 K for specific cluster geometries. For argon, the liquid induced potential barrier is only 0.7 K and it has a rather large amount of excess energy available along the recombination coordinate indicating that it is not possible to stabilize argon atoms in superfluid helium. Atomic fluorine shows the most pronounced effect with the recombination barrier of 26.8 K for producing ground state F₂. It is concluded that neon and fluorine atoms are good candidates to form impurity based quantum gels in bulk superfluid helium.     

Extremely Fast 1 μmol · mol−1 Water-Vapor Measurement by a 1 mm Diameter Spherical SAW Device

When a surface acoustic wave (SAW) is excited on a spherical surface, a naturally collimated SAW propagates around the equator hundreds of times. The propagation characteristics such as the velocity and amplitude are affected by adsorbed and/or reacted molecules on the surface, and the changes are accumulated by multiple turns of propagation. This enables highly sensitive detection of adsorbed molecules including water vapor. In this paper, the development and testing of a 1 mm diameter spherical SAW sensor, which is capable of measuring water vapor at concentrations well below 1 μmol · mol^?1H₂O in N₂, are reported. The rise time from 10% to 90% of the spherical SAW sensor to a step change from dry N₂ to 1 μmol · mol^?1H₂O in N₂ was approximately 15 s.     

Simultaneous Measurement of Torsional Oscillator and?NMR in Solid 4He with 10?ppm of 3He

We have performed the simultaneous measurement of torsional oscillator and NMR in solid ⁴He with 10 ppm of ³He at 3.6 MPa. In this solid, NCRI response appears below about 400 mK. NMR measurement shows that there is the same kind of phase-separated ³He cluster which is found in our previous measurement in solid ⁴He with over a hundred ppm of ³He. When we warm the solid above the phase separation temperature, the cluster disappears gradually. Below and above the phase separation temperature, the distribution of ³He atoms changes significantly with long time constant, which is as long as a day. However, even in such a long time span, we do not observe any systematic changes in the torsional oscillator response. This result suggests that the phase separation and related changes of the distribution of ³He is not directly related to the impurity effect of the NCRI response.     

Delocalization via Sliding in Solid 4He: Is It Plausible?

The modified Debye approach was used to calculate the Gibbs free energy for solid ⁴He and energetic profiles for different atomic displacements with respect to an equilibrium lattice. Atoms interact via the applied Aziz potential. We have found that individual atomic displacements may hardly give rise to any delocalization because of huge barriers but cooperative plane sliding is highly plausible especially in the intermediate phase, which was found to be more favorable than hcp for small cluster sizes. In the latter case the roughness of the potential profile is less than one kelvin. In some particular sliding cases the energy levels in the nearest wells nearly coincide that is a well-known precursor for the delocalization effect.     

Frequency and Size Dependences of Superfluidity in?Low-Dimensional 4He Fluids

We have studied superfluidity of ⁴He fluids in two- and one-dimensional states. In the 2D state of the ⁴He films on flat substrate, superfluidity was observed in the normal fluid state above the 2D Kosterlitz-Thouless temperature at high measurement frequencies. The superfluidity in 2D also depends on the system size, e.g. pore diameter of porous glasses and grain size of powder. The 1D state was realized for ⁴He fluid nanotubes formed in 1D nanopores 1.8?C4.7 nm in diameter and about 300 nm in length. Superfluidity in the 1D state was observed by the torsional oscillator experiment. The results are qualitatively well reproduced by the Monte Carlo calculation for a classical XY spin system modeled on the present ⁴He nanotubes. Although the 1D state is in the normal fluid state at any finite low temperatures due to the 1D phonon fluctuation, the superfluid frequency shift ??f of the oscillator can be observed. Above a temperature, ??f decreases due to another kind of 1D thermal fluctuation of which excitations destroy the phase coherence in the nanotubes. The excitations depend on the tube length as well as the tube diameter.     

Excitation of Narrow‐Band Pulsations in a Short Portion of Transition from the Smaller Diameter of a Pipe to a Larger Diameter and Possibilities of Preventing Them

By using models of the portions of the circuit of main gascompressor stations, data on the frequencies of narrowband pressure pulsations have been obtained; these data demonstrate the jet character of flow in divergent channels with angles of opening on one side of 12°47 and 23°50. It has been shown that narrowband acoustic disturbances are generated in the internal flow with largescale hydrodynamic structures. Intense narrowband pulsations are prevented by a grid of internal divergent channels in the transition portion with small angles of opening in canals and in excitation of certain disturbances upstream of a short divergent channel.     

History Dependence of Turbulence Generated by a Vibrating Wire in Superfluid 4He at 1.5 K

We report on the onset of turbulence in normal and superfluid ⁴He using several 13.5 μm diameter vibrating wire resonators placed in a cell, filtered from the surrounding helium bath. We measured the force-velocity characteristics of the wires in normal and superfluid helium over a velocity range up to several meters per second. The transition from laminar to turbulent behavior can be clearly identified. Surprisingly we find that, depending on the cooling history, turbulence in the superfluid does not always develop fully.     

Particles-Vortex Interactions and Flow Visualization in 4He

Recent experiments have demonstrated a remarkable progress in implementing and use of the Particle Image Velocimetry (PIV) and particle tracking techniques for the study of turbulence in ⁴He. However, an interpretation of the experimental data in the superfluid phase requires understanding how the motion of tracer particles is affected by the two components, the viscous normal fluid and the inviscid superfluid. Of a particular importance is the problem of particle interactions with quantized vortex lines which may not only strongly affect the particle motion, but, under certain conditions, may even trap particles on quantized vortex cores. The article reviews recent theoretical, numerical, and experimental results in this rapidly developing area of research, putting critically together recent results, and solving apparent inconsistencies. Also discussed is a closely related technique of detection of quantized vortices by negative ion bubbles in ⁴He.     

Mass Coupling and Q ?1 of Impurity-Limited Normal 3He in?a?Torsion Pendulum

We present results of the Q ^?1 and period shift, ??P, for ³He confined in a 98% nominal open aerogel on a torsion pendulum. The aerogel is compressed uniaxially by 10% along a direction aligned to the torsion pendulum axis and was grown within a 400???m tall pancake (after compression) similar to an Andronikashvili geometry. The result is a high Q pendulum able to resolve Q ^?1 and mass coupling of the impurity-limited ³He over the whole temperature range. After measuring the empty cell background, we filled the cell above the critical point and observe a temperature dependent period shift, ??P, between 100?mK and 3?mK that is 2.9% of the period shift (after filling) at 100?mK. The Q ^?1 due to the ³He decreases by an order of magnitude between 100?mK and 3?mK at a pressure of 0.14??0.03?bar. We compare the observable quantities to the corresponding calculated Q ^?1 and period shift for bulk ³He.     

Polarization Induced Spin Wave Damping in Spin Polarized Liquid 3He–4He

We have measured the temperature and polarization dependence of Silin spin wave spectra in a saturated ³He–⁴He mixture with a concentration of 9.4% at a pressure of 8 bars. The mixture has been cooled and polarized by a Leiden dilution refrigerator to temperatures in the range 10–15 mK and polarizations as high as 9.2% corresponding to 3.4 times the equilibrium polarization of 2.7% in the external magnetic field of 11.36 T. The analysis takes into account the dipolar interactions and results in the relaxation time τ _⊥ and spin diffusion constant D _⊥ . We find that τ _⊥ and D _⊥ are proportional to where T is the temperature, is the polarization enhancement factor and T _a0 is the anisotropy temperature for the mixture at equilibrium in the external field. Our result T _a0=3.66±0.14 mK is 30% higher than the theoretical prediction for very dilute mixtures and is evidence for the existence of polarization induced relaxation of transverse spin currents.     

Simulations of Non-linear Spin Dynamics in Spin Polarized Dilute 3He–4He Mixtures

Studies of spin dynamics of highly polarized dilute mixtures of ³He in superfluid ⁴He have been performed by various researchers over the past three decades. One series of experiments performed at Cornell University in the early 1990’s revealed a novel long timescale excitation. We present the numerical solution of the non-linear Leggett spin dynamics equation in one spatial dimension subject to boundary conditions consistent with the Cornell experiments. Experimentally observed phenomena are composed of trains of bursts in the transverse magnetization lasting several seconds. The simulations capture the time evolution of the individual bursts localized in time. Preliminary results of two dimensional simulations are also presented.