Roton backflow and the temperature dependence of the static structure factor of superfluid4He

The temperature dependence of the static structure factor of superfluid⁴He is given an interpretation in terms of the Feynman-Cohen picture of the elementary excitations by constructing the corresponding microscopic density matrix and including the effect of three-body terms. The required information on the ground-state wave function is taken over from configurations drawn from a Green's Function Monte Carlo computation. Correlations become stronger at finite temperatures in agreement with experiment. Backflow has only a modest effect onS(k, T).     

Density functional calculations for the structure of vortices in superfluid4He

The structure of a rectilinear vortex in superfluid ⁴ He at zero temperature is studied using a Density Functional method. The superfluid circulation is included via the Feynman-Onsager approximation. The energy and the density profile of a vortex are predicted for several values of the external pressure. The instability of the vortex line at negative pressure is discussed.     

Frequency dependence of superfluid onset temperature of4He films on oscillating substrates

We have studied the frequency dependence of the superfluid onset for⁴He films on Mylar substrates using a two-torsional-oscillators technique. A peak of the dissipation accompanied by the superfluid onset appears at higher temperatures for 2009 Hz than for 530 Hz. The temperature difference T_p between the two peaks is 2.0 ± 0.5 mKfor coverages with the onset temperature T_c of 1.4 K, and increases by a factor of three with decreasing T_c from 1.4 to 0.95 K. In the temperature dependence of the dissipation, the dissipation width also increases by a factor of three with decreasing T_c from 1.4 to 0.95 K. The T_c dependencies of T_p and the dissipation width indicate that an intrinsic parameter D/r₀ ² of a vortex decreases with the superfluid onset temperature, where D is a diffusion constant and r₀ a core radius.     

Temperature dependence of the condensate fraction of superfluid4 He

The roton contribution to the temperature dependence of the condensate density is discussed. The analysis is carried out through the inclusion of a gauge symmetry breaking field. Under the hypothesis that the thermal excitation of rotons is the main responsible for the depletion of the condensate, we obtain an explicit result for the temperature dependence of the condensate density which rather well agrees with the available experimental data.     

Flow dependence of spin susceptibilities in superfluid3He

The flow dependence of spin susceptibilities in superfluid ³ He-A and -B is studied theoretically. It is shown that in the A phase _A, the component of the static spin susceptibility parallel to , increases rapidly in the presence of mass current. A similar behavior is found for all components of _B, the susceptibility tensor of the B phase.Work supported by the National Science Foundation under grant No. DMR76-21032.Recipient of a scholarship from the Studienstiftung des Deutschen Volkes.     

Solitons in superfluid 4He films

The Korteweg-de Vries (KdV) equation is derived from Landau two-fluid hydrodynamics applied to the thickness oscillation of the superfluid ⁴He film at low temperatures, where the main restoring force is van der Waals attraction from the substrate and the thermomechanical force due to phonons is a small correction. Since the usual third-sound generators and detectors are far wider than the individual solitons, the asymptotic solution of the KdV equation provided by the inverse scattering method is coarse-grained by regarding it as a continuous train of sharp pulses. The envelope so obtained still shows a singular front proportional to (t–t ₀)^–1/2, where t ₀ is the arrival time of the fastest soliton, and should therefore be observable with the appropriate experimental arrangement.     

Stability,orientational effects,and temperature dependence of nonunitary vortex structures in superfluid3He

First we set up the nine Ginzburg-Landau (GL) equations for the ninecomplex radial functions of an axisymmetric vortex line in superfluid³He. These GL equations necessarily yield a nine-componentnonunitary state for the A-phase vortex that corresponds to the Mermin-Ho trial state. We then solve the GL equations and calculate the energies for the five B-phase vortices of different symmetries that have been discussed by Salomaa and Volovik. We find that the only stable vortex is theirv-vortex, which has a superfluid and ferromagnetic core. Theo-vortex, which has a normal core, turns out to bemetastable (it is a saddle point on the energy surface describing theuvw-vortices). Theu-,w-, anduvw-vortices are found to beunstable. In the second part of the paper we calculate, with the help of the generalized GL theory, the temperature corrections to the GL structures of theo- andv-vortices. It turns out that the corresponding temperature variations of the two orientational energies for the -vector that are linear and quadratic in the field disagree with the measured temperature variations of the parameters and (see Hakonenet al.). However, a novel new orientational energy due to the interaction of the field and superflow around the vortex line increases linearly asT is decreased, in agreement with the measured behavior of .     

Depression of the superfluid transition in4He

We study superfluid⁴He near T in a homogeneous metastable state where a finite superfluid velocity v_s is present. Neglecting vortices we perform a renormalization-group calculation of the critical velocity v_sc(T) at which the superfluid state becomes unstable. We apply this result to the situation where the superfluid velocity is induced by a finite heat current Q. A critical heat current Q_c(T) corresponding to v_sc(T) is found which implies a transition temperature T (Q)=T[1–A_oQ^x]. We determine the exact exponent x=[(d–1)v] ^–1 0.744 in d=3 dimensions and calculate A_o in one-loop order. Our results for A_o and x are compared with recent experimental data.     

Dispersion of ripplons in superfluid4He

The excitations of the free surface of liquid⁴He at zero temperature are studied, with special emphasis to the short wave length region. The hybridization mechanism between surface and bulk modes is discussed on a general basis, investigating the scattering of slow rotons from the surface. An accurate density functional, accounting for backflow effects, is then used to determine the dispersion of both bulk and surface excitations. The numerical results are close to the experimental data obtained on films and confirm in an explicit way the general reflection mechanism exhibited by rotons. Moreover they reveal the occurrence of a damped ripplon branch above the roton threshold.     

Measurements of superfluid densities and critical superfluid mass currents of pure 4He and 3He/4He mixtures in nuclepore near the lambda transition

Measurements have been made of the relative superfluid density _sp/ and the critical mass current I _sc for the onset of dissipation in the superfluid flow of pure ⁴He and ³He/⁴He mixtures in the circular cylindrical pores of Nuclepore near the transition, using a double-ended Helmholtz resonator. Pore diameters of 0.03, 0.1, and 0.4 m were studied using ³He mole fractions of 0.0,0.2, and 0.4. For each pore diameter d _p and mole fraction x our results for _sp / were fitted relatively well by the form C(t – t ₀₁)^0.675 and those for I _sc by the form I _sc0(t–t _0c ) ^g , where t [T –T]/T . For each combination of d _p and x the reduced onset temperatures t ₀₁ and t _0c are in rough agreement with each other but somewhat larger than values found by others for Nuclepore. For the smaller two pore diameters, these onset temperatures are consistent with the universality hypothesis that near T, ² _sb /m ₄ ² k _B T should be a constant independent of T and x. Here is the reduced Planck constant, _sb is the bulk superfluid density, is the coherence length, m ₄ is the ⁴He atom mass, k _B is Boltzmann's constant, and T is the absolute temperature. At each value of x the amplitudes C agree well with the corresponding amplitude for _sb /, and g equals 1.17 ± 0.04 for all cases. Measurements of the velocity of second sound at x = 0.000, 0.190, 0.401, and 0.450 are also reported.Work supported by U.S. Department of Energy contract EY-76-S-02-1569.     

A novel He3He4 dilution refrigerator with superfluid He4 circulation

A novel dilution refrigerator system is proposed, which offers the potentiality of very high circulation rates. The design of this refrigerator is described and the construction and performance of a prototype are discussed. He⁴ is circulated by means of a multi-stage thermomechanical or fountain pump, which can build up high fountain pressures.     

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

The thermal conductivity of³He–⁴He solutions at saturated vapor pressure has been measured for the concentration range 0.011–1.3 mole %³He and the temperature range 84–650 mK. Measurements were made at 10 and 24 atm for several of the concentrations. The thermal conductivity of solutions at 24 atm does not differ greatly from the thermal conductivity of pure⁴He at this pressure. Qualitative agreement with the Baym and Ebner theory is achieved only if the boundary scattering of phonons is treated in a different manner than suggested by them.     

Static response function in superfluid4He

Rigorous lower and upper bounds for the static response function in superfluid⁴He at zero temperature are derived using a sum rule approach. The ingredients needed to calculate the bounds are taken from recent Monte Carlo simulations for the ground state. The new bounds improve significantly the Feynman approximation and provide estimates of the static response function in agreement with the experimental data at zero pressure.     

Critical temperature and critical current of thin-film superfluid3He

Superfluid³He film flow over the rim of a copper beaker has been measured. The flow rate was measured as a function of temperature and as a function of depth of³He below the rim or film thickness at the rim. The critical current, calculated from the flow rate, varied as (1 –T/T _c ^p )^3/2 as expected for pair-breaking;T _c ^p is a film-thickness-dependent critical temperature. However, the magnitude of the current was an order of magnitude smaller than expected for pair-breaking, in agreement with other experiments that have demonstrated a lower dissipation mechanism in superfluid³He. The suppression of the critical temperatureT _c ^p /T _c ^b , whereT _c ^b =0.93 mK is the bulk³He transition temperature, varied from 0.93 to 0.7 as the film thickness at the rim varied from 120 to 90 nm. These ratios are larger than expected from Ginzburg-Landau or microscopic theory of superfluid³He-B.Deceased 19 June 1987.     

Measurement of the surface tension of superfluid4He at low temperature by capillary wave resonances

The surface tension of liquid⁴He is determined from the frequencies of micron wavelength capillary waves. The extrapolated zero temperature value, σ=375±3 μJm⁻², is in agreement with the pioneering static capillary rise determination but 6% higher than the more recent surface tension gravity wave measurements. Flow in the meniscus in this latter experiment is shown to mimic a surface tension correction to the dispersion relation there used which is of the same sign and magnitude as the discrepancy.     

Density and temperature dependence of the momentum distribution in liquid helium 4

Deep inelastic neutron scattering measurements on liquid⁴He have been carried out for temperatures from 0.35 K to 4.2 K and densities from 0.125 to 0.200g/cm³ at a momentum transfer of 23 Å^–1. These measurements are at large enough momentum transfer that deviations from the Impulse Approximation are accurately described by current theories and information on the single particle momentum distribution may be extracted from the measured scattering. The scattering exhibits non-Gausian behavior in both the normal liquid and superfluid phases. A distinct change in the scattering, marked by a reduction in the width and increased deviations from the classical Gaussian shape, occurs at the suerfluid transition. We present a comparison of our experimental results with recent calculations at a variety of temperatures and densities and show that theory and experiment are in excellent agreement. We also present model scattering functions, obtained by correcting for instrumental resolution and final state effects, that represent the scattering in the IA limit. Finally, we present values for the average kinetic energy and the Bose condensate fraction over a broad range densities and temperatures.     

Variational theory of rotons in superfluid4He

We have extended the shadow wave function for excited states by including an explicit backflow term in the shadow variables. The variational computation gives a roton energy 9.18 K, only 6% above experiment. Similar agreement is found at freezing density. Also the strength Z_q of the single excitation peak greatly improves. The uniform agreement between theory and experiment at all wave vectors suggests that there is no qualitative difference in the wave function of phonon, maxon and roton excitations. Only the amount of backflow and short range correlations greatly varies with k.     

Spreading of superfluid4He on MgF2

We have investigated the spreading of superfluid⁴He on top of a polished fused silica plate which is coated by a thin layer of MgF₂. Our interferometric experiments indicate that a superfluid⁴He film of about 100 nm thickness is not able to spread uniformly over a nearly horizontal substrate, and hence these films cannot be governed by the Van der Waals forces only. Even in the stationary state, we observe nonzero (1 – 20 mrad) contact angles which display hysteresis, spatial variation, and strong history dependence.