Ginzburg-Landau free energy in superfluid3He

The Ginzburg-Landau free energy in superfluid³He is derived from kinetic theory.     

Comment on the specific heat of superfluid 3He

We present numerical results for the specific heat of ³He-B in the weak-coupling-plus model. We find that the full temperature dependence of the specific heat is accurately determined by the specific heat jump at T _c .This provides a test of the T _c /T _F expansion scheme for calculating strong coupling effects in superfluid ³He.     

Anomalous specific heat of liquid 3He above the superfluid transition temperature

The contribution to the specific heat due to order parameter fluctuations in liquid ³He just above the superfluid transition temperature T _c is calculated exactly within a Landau theory approach. The effect turns out to be unobservably small and thus cannot explain the large (9%) rise in specific heat above the normal state value at the saturated vapor pressure in a recently reported experiment. We do not find the divergence of the specific heat at T cobtained earlier by Thouless from a microscopic calculation and indicate how the difference can be reconciled.     

Generalized Ginzburg-Landau theory for superfluid He and application to Helical textures in 3He-A

We first discuss the generalized Eilenberger equations for superfluid ³He in the presence of a magnetic field and for uniform rotation of the system. These equations determine the space-dependent Green's function, the free energy density, and the supercurrent density at all temperatures. From these equations we derive the generalized Ginzburg-Landau series expansions in powers of spatial derivatives and the order parameter. This is in contrast to Cross' generalized Ginzburg-Landau approach, which takes into account only spatial derivatives up to second order. Explicit expressions are given for the corrections of order (1 – T/T _c)to the well-known expressions for the bending energy, magnetic anisotropy energy, and superfluid current. With the help of these expressions we calculate the stability regions of uniform and helical textures in the superflow-field phase diagram. For decreasing temperature these regions are found to become smaller. The stability region of the uniform texture vanishes at T _h ⁰ - 0.88T _c], in agreement with Fetter's result.     

Specific heat of normal and superfluid3He

Extensive measurements of the heat capacity of liquid ³ He in the normal and superfluid phases are reported. The experiments range from 0.8 to 10 mK and cover pressures from 0 to 32.5 bar in zero magnetic field. The phase diagram of ³ He, based on the platinum NMR temperature scale, is presented. In the normal liquid at low pressures and near the superfluid transitionT _c an excess specific heat is found. The effective massm* of³He is at all pressures about 30% smaller than the values reported earlier. The calculated Fermi liquid parameters F₀ and F₁ are reduced asm*/m, while the spin alignment factor (1 + Z₀/4)^–1 is enhanced from 3.1–3.8 to 4.3–5.3, depending on pressure. The specific heat discontinuity C/C atT _c is forP = 0 close to the BCS value 1.43, whereas at 32.5 bar C/C is 1.90±0.03 in the B phase and 2.04±0.03 in the A phase, revealing distinctly the pressure dependence of strong coupling effects. The temperature dependence of the specific heat in the B phase agrees with a model calculation of Serene and Rainer. The latent heatL at the AB transition is 1.14±0.02 µJ/mole forP = 32.5 bar and decreases quickly as the polycritical point is approached; at 23.0 bar,L = 0.03 ± 0.02 µJ/mole.Work supported by the Academy of Finland.     

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.     

Hydrodynamic heat flow in very dilute superfluid3He-4He mixtures

The superfluid hydrodynamics of heat flow is examined for very small mass concentrationsc of³He in⁴He in an effort to better understand recent results for the effective heat conductivity _eff, which appear to be in conflict with predictions. The full hydrodynamics contains a thermal boundary layer; within this layer the temperature and concentration gradients differ from those in the bulk fluid. An examination of finite heating effects based on the ansatz _eff c ^–p for smallc shows distinctly different behavior for experimental determinations of _eff whenp<1,p=1, andp>1. Thus, finite heating can be used as a probe to evaluate the exponentp.     

Sum rules for a binary solution and effective interactions between3He quasiparticles in superfluid4He

Sum rules are derived for dynamic structure factors for a binary solution and applied to the Woo-Tan-Massey theory of ³ He- ⁴ He solutions. We demonstrate that in the long-wavelength region the effective ³ He quasiparticle interactionV _k contains no lineark dependence. In other words, $$V_k \to A + Bk^2 {\text{ }}as k \to 0$$ This result is exact, and requires no empirical information. It is consistent with expressions ofV _k assumed by Eckstein, Eckstein, Kuper, and Ron, and by Ebner, based on fitting experimental data such as osmotic pressure measurements.     

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.     

Heat flow in superfluid 3He

The thermal resistance in both superfluid phases of ³He has been measured at 20.0 and 29.6 bar in zero magnetic field. Heat conduction in ³He-B is shown to be primarily hydrodynamic, and a regime of reproducible heat flow behavior in the A phase is reported. The viscosity of each phase as a function of temperature is calculated using an equation of the two-fluid model, and critical velocity effects are discussed.Work supported by the U.S. Atomic Energy Commission under Contract No. AT(04-3)-34 P.A. 143.     

Persistent currents in superfluid3He

Measurements are reported of persistent currents in superfluid³He-B and³He-A. An ac gyroscope filled with 20 µm powder and mounted into a rotating nuclear refrigerator was employed. In³He-B, undiminished circulation was observed for 48 h; this implies an effective viscosity at least 12 orders of magnitude lower than in the normal fluid at the same temperature. AtP<15 bar, the observed critical velocity is independent of temperature but it is a weak function of pressure;v _c varies between 4 and 6 mm/sec. The response to rotation is hysteretic, with elastic potential flow at slow rotation and irreversible vortex flow at higher angular velocities. The persistent angular momentumL is reversible when thermally cycled in the B phase, and proportional to the superfluid fraction _s /. Above 15 bar the B phase splits into separate regions with different critical velocities. The measuredv _c in the phase existing only at high pressures is dependent on magnetic field; for example, at 23.0 bar,v _c (H=0) =5 mm/sec, butv _c (H=40 G) =15 mm/sec. In the low pressure phase,v _c is insensitive to a change in the magnetic field. The phase transition is of first order; the latent heatQ _G (1 µJ/mole) depends on the maximum angular velocity at which the cryostat was rotated. The transition is proposed to occur in the core structure of pinned quantized vortices sustaining persistent currents. In³He-A, currents could not be found to persist on an observable level. Direct measurements ofL atH=0 and atH=40 G, and repeated thermal cycling, showed that either the current decays rapidly orv _c <0.5 mm/sec.     

Orbital modes in superfluid3He

The equation describing the rotation of the orbital coordinate in superfluid³He is obtained. It is shown that the orbital modes obey a diffusion-like equation with a finite energy gap. The transient behavior of the vector in the A phase after thed vector is suddenly rotated is considered.Supported by the National Science Foundation.On leave from Department of Applied Science, Tohoku University, Sendai, Japan.     

Static magnetization of superfluid 3He

New measurements of the static magnetization of ³He-B in contact with a variety of wall configurations are presented and compared with previous measurements in both A and B phases. At high pressure the data tend toward agreement with resonant-magnetism experiments, while near the polycritical point a large discrepancy between the results of the two methods remains.Supported by the U. S. Energy Research and Development Administration under contract no. EY-76-S-03-0034, P.A. 143.     

NMR in flowing superfluid 3He

The effects of flow on the NMR absorption in the A and B phases of ³He have been studied. While no flow-induced changes in the absorption were seen in the B phase, a variety of phenomena were observed in the A phase. The phenomena include the development of time-dependent satellite peaks, height reductions of the signal, and a splitting of the signal, with a fraction of the signal shifting to lower frequencies. These effects are described and discussed in light of the existing theoretical models. In addition, the NMR shift in the static B-phase liquid confined between 135-m-spaced parallel plates has been measured as a function of temperature and the angle between the magnetic field and the plates. These results are compared with previous measurements and are found to be in good agreement. Finally, two effects observed in the static liquid, the disappearance of the B-phase signal under certain conditions and the splitting of the A-phase signal, are described.Research supported by the National Science Foundation.     

Zero-sound studies in superfluid 3He

The propagation of 5-, 15-, and 25-MHz sound in superfluid ³He has been studied in zero magnetic field over a wide pressure range. Measurements of the structure and location of the attenuation peaks, velocity changes, and the low-temperature attenuation are described. The degree of strong coupling in the B phase is discussed. Observations of superheating and supercooling near the polycritical point have been extended and comparison is made with theory.Work supported by the U.S. Energy Research and Development Administration under Contract No. E(04-3)-34, P.A. 143.     

The vortices of superfluid 3He

In the superfluid phases of ³He quantized vortex lines have been investigated under uniform rotation, when they form a regular array of rectilinear objects. A large diversity exists in the structure and properties of vortices, owing to the complicated nature of symmetry breaking in the different superfluid phases. A review is presented here on the various experimentally verified types of vortices. Recent measurements open a puzzling problem about their interaction and interconnection at the first-order phase boundary separating the A and B phases of superfluid ³He.An invited contribution to the Symposium on Quantum Fluids and Solids 1992, June 15–19, Pennsylvania State University, University Park, Pennsylvania 16802.     

Spin waves in anisotropic superfluid3He

Spin waves in the A phase of superfluid³He are studied theoretically. It is assumed that the condensate in the A phase consists of theP-wave triplet pairs of the type suggested by Anderson and Brinkman. We show that the spin wave mode with a finite energy gap exists throughout the A phase. In particular atT=0 K the dispersion of the spin wave is given by, forvq<Δ, $$\omega ^2 = \omega _0^2 + 2(1 - \bar I)A\Delta ^2 + \tfrac{1}{3}(1 - \bar I)v^2 q^2 $$ where θ is the spin wave energy, ω _T =[ω ₀ ² +2(1?ī)AΔ²]^1/2 is the nuclear magnetic resonance energy,v is the Fermi velocity,q is the wave vector of the spin wave, andī=IN(0)=?1/4Z ₀ is the Landau-Fermi liquid parameter.     

Pulsed NMR studies of superfluid3He

We present a review of our pulsed NMR experiments in the A and B phases of superfluid³He, at pressures of 23 and 27 bar. We have measured the dipole frequency in³He-A, spin susceptibility in³He-B, and tip-angle-dependent frequency shifts in both phases. In general, we find excellent agreement with results by other workers. In³He-B, complex spin motions were observed involving long-lived free induction decays with a time-dependent precession frequency. Spin relaxation measurements for both³He-A and³He-B are discussed and compared with those of other workers. After driving the magnetization far from equilibrium, anomalous frequency shifts were found to persist in the A phase. We discuss a soliton-texture model by Bruinsma and Maki which accounts for these resonances.Work supported by the National Science Foundation Grant DMR-78-10901 and through the Cornell Materials Science Center through NSF Grant DMR-79-24008 A02. (MSC Report #4459).     

Spin-independent transport parameters for superfluid3He-B

The scalar kinetic equation for Bogoliubov quasiparticles in the B phase of superfluid³He is discussed and the collision integral is represented in a compact form. For the cases of shear and second viscosity and diffusive thermal conductivity the problem is reduced to solving one-dimensional integral equations. The quasiparticle interaction enters via weighted angular averages of the normal state scattering amplitude. The effect of strong coupling renormalization of the gap function is accounted for. The transport coefficients are exactly related to relaxation parameters that describe how the system tends toward local equilibrium. For low temperatures the transport parameters are evaluated exactly, including corrections of orderT/T _c. The results are compared with those of a previous paper in which an approximate form of the collision operator was used, as well as with results of a variational approach and with recent experimental data.