Magnetic excitations in superfluid 3He

Localized magnetic excitations (solitons) in superfluid ³He are studied theoretically. In the A phase, we determine the dispersion of solitons in both the longitudinal and the transversal configurations, while in the B phase we limit ourselves to the longitudinal soliton in the Leggett configuration. In the wall pinned configuration of the B phase we show that the magnetic perturbation propagates as spin wave. The effects of the spin-diffusion term on solitons as well as spin waves are considered. The soliton velocity decreases exponentially in time owing to the spin-diffusion term with a characteristic time % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% qedmvETj2BSbacfaGae83KdCKae8hiaaIae83waSLaeyyyIORaaiik% aiaaiodacaGGPaGaaiikaiaadogadaahaaWcbeqaamaaCaaameqaba% GaaGOmaaaaaaGcciGGVaGaamiraiabfM6axnaaCaaaleqabaWaaWba% aWqabeaacaaIYaaaaaaakiaacMcacaGGDbaaaa!4DB4!\[\Gamma [ \equiv (3)(c^{^2 } /D\Omega ^{^2 } )]\] where D is the spin-diffusion constant, is the Leggett frequency, and c is the spin-wave velocity.Supported by the National Science Foundation.     

The proximity effect between superfluid3He and a3He-4He mixture

The quasiclassical theory is used to study the proximity effect between superfluid ³ He and a mixture of ³ He- ⁴ He. The order parameter and the surface tension are calculated, and their dependence on temperature and on the hypothetical transition temperature of the ³ He- ⁴ He mixture is discussed.     

Propagation of solitary waves in a mixture of liquid3He and superfluid4He

The effect of an admixture of liquid³He on the propagation of solitary waves in superfluid⁴He is investigated. In the local density approximation, the mean field equations are reduced to the two-fluid equations describing the dynamics of the mixture of two liquids. The nonlinear perturbation approach is used to obtain a set of equations describing the density and velocity fluctuations of the homogeneous mixture at rest. The self-consistent solution of these equations is shown to be the solitary waves. Using a pseudopotential method, we perform numerical calculations to study the changes in the general properties of the waves caused by the³He impurity.     

Convective instability of a superfluid3He-4He mixture in a superleak

The convective instability of a superfluid³He-⁴He mixture in a porous medium confined between parallel horizontal planes is studied. It is shown that this system behaves as a pure classical liquid in a porous medium from the point of view of the convective instability in the whole range of the phase diagram between the λ line and the coexistence curve. It is predicted that two-fluid effects become important for the convection onset and can be observed experimentally in this system at moderately low temperatures. This system is supposed to be the most convenient one to study experimentally convection in a porous medium.     

The collective excitations of superfluid4He in aerogel glass

When liquid⁴He is condensed in porous aerogel glass (typical pore size ≈ 500 Å), many of the superfluid properties are significantly altered. Neutron inelastic scattering has been used to measure the collective phonon-roton excitations of liquid⁴He in this restricted geometry. Although at low temperature (1.3 K) the observed dispersion relation is identical to that of bulk⁴He, its temperature dependence is shown to be different. Previously unexplained superfluid fraction data are shown to be derivable from these microscopic measurements. An intrinsic broadening of the excitations associated with the restricted geometry is also present. Possible microscopic explanations for the unusual temperature variation of the collective excitation energies are discussed.     

Thermal convection and nonlinear effects of a superfluid3He-4He mixture in a porous medium

The convective instability of superfluid³He-⁴He mixtures in porous media is investigated. The general hydrodynamic equations are derived and reduced to a single nonlinear equation for a scalar field. The superfluid mixtures in a porous medium have a constant⁴He chemical potential and behave essentially like a classical fluid in a porous medium. Two-fluid effects are calculated both at the onset of steady convection and the subsequent boundary of instability. The shift of critical Rayleigh number is about 1% or less at the onset of convection, but can be as large as 20% or more at the instability boundary for some regions aroundT 1 K. This two-fluid shift is quite large compared to the corresponding 0.001% shift at the onset of convection for bulk superfluid³He-⁴He mixtures.     

Bound states of one-particle excitations in superfluid3He near walls

It is argued that a large number of bound states with energy below the gap can exist near the walls of a vessel containing superfluid³He. This is due to the decrease of the energy gap near the walls. Bound states can exist in both B and A phases.     

3He impurity excitations in solid4He

The problem of³He mobility in dilute³He-⁴He solid mixtures has been treated both theoretically and experimentally. The Hamiltonian of the system can be reduced to the Hamiltonian of strongly interacting impurity quasiparticles corresponding to some time-averaged states. The experiments carried out on solid mixtures with³He concentration 2.17%, 0.75%, 0.25%, or 0.092% by the NMR method show that at sufficiently low (T<1.2 K) temperatures the diffusion coefficient becomes temperature independent and inversely proportional to³He concentration. These results substantiate qualitative conclusions of the theory. Analysis of the experimental data makes it possible to take into account the phonon part of the³He diffusion coefficient and to obtain, up to a constant, the³He-⁴He exchange energyJ10^–7 K. All the facts mentioned above testify to the substantially quantum nature of the³He diffusion process in dilute³He-⁴He mixtures.     

Generation of intrinsic excitations in superfluid 4He by using gas jet approach

No Heading A radio frequency discharged helium gas jet was used to generate intrinsic excitations in bulk superfluid ⁴He. The present experimental results and our previous estimates show that metastable triplet state He atoms and excimers cannot enter directly the liquid but rather concentrate on the liquid surface. High concentration of metastable species promotes reactions, which then lead to formation of He ions. Upon electron - ion recombination, population of highly excited atomic and diatomic excimer electronic states occurs. Effect of molecular hydrogen on quenching of the helium emissions is demonstrated. Excitations are efficiently transferred from He to H₂.PACS numbers: 33.20 Kf, 33.70 Jg.     

Neutron scattering as a probe of particle-like excitations in superfluid4He: A model calculation

In the microscopic theory of Bose-condensed liquids, the condensate wave function leads to a coupling of the density fluctuations and the single-particle excitations. A simple parametrized model of this based on coupling weakly damped zero-sound modes with strongly damped free-particle-like excitations Q ²/2m* explains why the phonon-roton resonance inS(Q, ) for superfluid⁴He exists above and belowT but only plays the role of an elementary excitation belowT . It is pointed out that this model also predicts thatS(Q, ) should exhibit a weak, low-frequency peak centered atQ ²/2m*, with weight roughly proportional to the condensate fractionn ₀. As a stimulus to further experimental searches for this branch, some model calculations are given forS(Q, ) forQ1 Å^–1.     

Second-viscosity phenomena in dilute solutions of3He in superfluid4He

A theory of second-viscosity phenomena in dilute solutions of³He in superfluid⁴He is presented. The theory considers only phonon and³He quasiparticle excitations and is therefore valid at temperatures below about 0.6 K. It is shown, by an exact calculation, that within the framework of the Landau-Pomeranchuck model for the³He quasiparticle excitation energy, the four second-viscosity coefficients are related to one another and that only one of them is actually an independent kinetic coefficient. The relations between the second-viscosity coefficients are applied to analyze the expressions for the dissipative function and the first- and the second-sound attenuation coefficients. It is shown that the second-viscosity contribution to the second-sound attenuation is smaller by an order of magnitude than its contribution to the first-sound attenuation.     

Heat transport in dilute mixtures of3He in superfluid4He

We report new measurements of the effective thermal conductivity K_eff and relaxation time τ in dilute mixtures of³He in superfluid⁴He, with molar concentrationsX≤10⁻³. The temperature range extended fromT≈1.4 K toT _λ. Both K_cff and τ are found to agree with theoretical predictions, in contrast to previous experiments where significant differences were observed. A new thermal conductivity cell design was used which almost completely eliminates extraneous volumes and surfaces, and the earlier results are explained in relation to these design changes.     

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.     

Time-dependent thermal convection in dilute solutions of 3He in superfluid 4He

Time-dependent thermal convection can occur in a unity-aspect-ratio Rayleigh-Beard convection cell containing a dilute solution of ³He in superfluid ⁴He when the fluid is heated from above. Results are presented primarily for a 0.24 mole % He solution at 0.925 K. Means is provided for introducing heat at the top and separately for a central plug and an outer ring such that both are at a constant temperature gDT above the bottom. A critical temperature difference T _cfor convection can be defined above which both steady and time-dependent convection occur. The time-dependent effects include a region of T. near T _cand characterized only by excessive noise, a region of somewhat higher T where there are intermittent major changes in the plug heating rate with a time distribution like that for random events, and a region at still higher T where periodic but nonsinusoidal variation of the heat flow is observed. When a long enough time, several months, has elapsed after cooling down the apparatus, time-dependent states no longer occur, and the heat flow above T _cis limited to steady convection. Briefly raising the temperature of the apparatus to 77 K is sufficient to restore the possibility of time-dependent states.     

Phase equilibrium in a polarized saturated3He—4He mixture

We present experimental results on the phase equilibrium of a saturated³He−⁴He mixture, which has been cooled to a temperature of 10–15 mK and polarized in a⁴He circulating dilution refrigerator to a stationary polarization of 15%, 7 times higher than the equilibrium polarization in the external field of 7 T. The pressure dependence of the polarization enhancement in the refrigerator shows that the molar susceptibilities of the concentrated and dilute phase of a saturared³He-⁴He mixture are equal atp=2.60±0.04 bar. This result affects the Fermi liquid parameters of the dilute phase. The osmotic pressure in the dilute phase has been measured as a function of the polarization of the coexisting concentrated phase up to 15%. We find that the osmotic pressure at low polarization (<7%) agrees well with thermodynamics using the new Fermi liquid parameters of the dilute phase.     

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.     

Bound states of3He in3He-4He mixture films

³He atoms dissolved in super fluid⁴He may form aimers (³He)₂ in twodimensional (2D) geometries. We study dimer formation in films of dilute³He-⁴He mixture. After designing a schematic³He-⁴He interaction potential we calculate the dimer binding energy for various substrates. It is shown that³He impurity states localized near the substrate give rise to the largest magnitudes of the binding energies.Unité de Recherche des Universités Paris XI et Paris VI associée au CNRS.