The superfluid transition temperature of liquid 3He

The superfluid transition temperature, T_c, is calculated from a scattering amplitude (constructed from the polarization potentials of Aldrich and Pines) which has been shown to yield agreement with experiment for transport properties. Our calculated values agree with experiment at all pressures up to 34 atm.     

Spin waves in anisotropic superfluid 3He

Spin waves in the A phase of the superfluid ³He are studied within a microscopic model. It is shown that the spin wave mode with a phonon like dispersion and a gap exists through out the A phase.     

Spectrum of 3He atoms in superfluid 4He

It is suggested that at a wave vector near the inverse average interparticle separation, the spectrum of a ³He atom in superfluid ⁴He has a roton like dip. The results of light scattering and transport measurements in liquid ³He-⁴He mixtures can thereby be reconciled.     

Bose spectrum of superfluid solutions 3He4He

The Bose spectrum of superfluid solutions ³He⁴He is investigated in the case of p-pairing of Fermi particles. Both three-dimensional and two-dimensional models are considered. It is shown that the Bose-Fermi interaction changes the sound velocities in both subsystems. The other collective modes (17 in the 3D-model and 11 in the 2D-model) remain almost unchanged.     

Superfluidity of 3He in dilute solutions of 3He in liquid 4He

The possibility of superfluidity of ³He in dilute solutions of ³He in liquid ⁴He is investigated, and the corresponding critical temperature is estimated. The results indicate S-state pairing, i.e., for small concentrations of ³He, the highest transition temperature is obtained for L = 0, but the obtained critical temperatures are very low.     

Thermodynamics of textures in superfluid 3He

The contribution of the textures in the B-phase of superfluid ³He to the specific heat has been calculated. The specific heat is found to be divergent near T_c.     

The quasiclassical approach to superfluid 3He

We develop the quasiclassical theory for normal and superfluid liquid ³He using a systematic expansion in small parameters such as δ/E_F, ?₀^?1/k_F, etc., and paying particular attention to the high-energy renormalizations of the external pertubations and observables. We apply the general formalism to a number of more specific problems including the derivation of the non-linear quantum kinetic equation for normal ³He, the weak-coupling and strong-coupling free energies and static response functions for superfluid ³He, and the low-frequency and high-frequency dynamics of the superfluid phases. We also discuss extensions of the quasiclassical framework to cover strong short-ranged pertubations such as walls and ions, review recent phenomenological models for the quasiparticle scattering amplitude, and present a brief but self-contained derivation of the Keldysh perturbation theory for real-time Green's functions.     

Pulsed NMR frequency shifts in superfluid 3He

We report the first measurements of the NMR frequency in ³He A and B under conditions where the net magnetization, M, is tipped far from its equilibrium direction along H_O. In ³He A the frequency shift ω - γH_O varies from the continuous wave value at tipping angle Φ = 0 to a negative shift at Φ = 180°. In ³He B no frequency shift is observed, however for Φ ? 100° a beat pattern is seen to develop in the free induction decay envelope.     

Transverse zero sound propagation in superfluid 3He

Transverse zero sound should propagate in superfluid ³He only in a rather narrow range below T_c.     

Hamiltonian equations of hydrodynamics of anisotropic superfluid liquid 3HeA

On the basis of the Hamiltonian technique equations describing hydrodynamics of anisotropic superfluid liquid ³HeA are obtained. The conservation laws are formulated. Expressions for dissipative terms are found.     

This mysterious liquid 3He

The spin contribution to the heat capacity and entropy of ³He has been singled out. With increasing T the spin entropy reaches a constant value, different from ln 2. The spin contribution ≈ ln T can be observed in the temperature dependence of the pressure.     

Quasiparticle interaction in liquid 3He

The quasiparticle interaction in liquid ³He is studied. It is shown that part of the interaction can be considered induced through the exchange of density and spin-density excitations. The coupling of these excitations to quasiparticles is shown to be given rigorously by the quasiparticle interaction itself in the long wavelength limit. The induced part of the interaction is then calculated by determining the density-density and spin-density-spin-density response functions assuming that the irreducible particle-hole vertex functions are frequency independent. The remainder of the interaction is shown to be given by a vertex function which does not have certain singularities and it is argued that it can be approximated by the Brueckner G-matrix. From the net interaction Landau parameters are extracted and compared with the experimentally known ones. Since the agreement was not satisfactory, the consequences of making a theory in terms of “paramagnons” is explored. This leads to much better numerical results, but the theory is less satisfactory. Consideration of the density-density response function arrived at here shows it to be similar to one proposed by Pines and Nozières [3, 24], who assumed a local relation between a density fluctuation and the potential it produces. We come to the conclusion that the numerical discrepancies between our calculated Landau parameters and the experimental ones probably arise from neglect of the exchange of two and more spin fluctuations. In the paper following this one, O. Sjöberg makes application of our theory to calculate the Landau parameters of nuclear matter. No “soft” excitations such as the spin fluctuations of liquid ³He exist in nuclear matter, and the theory appears to be quantitatively much better there, although some of the crucial Landau parameters are not directly measurable, and a direct check is not possible.     

The first-to-zero-sound transition in non-superfluid liquid 4He

Neutron inelastic scattering from ⁴He at T = 2.3 K shows that for Q ? 2 nm^?1 “sound-wave” excitations propagate with the characteristics of ordinary or first sound while for Q ? 3 nm^?1 they propagate with the characteristics of zero sound.     

Anomalous nuclear spin relaxation in liquid 3He4He mixtures

The longitudinal relaxation time, T₁, was measured in liquid ³He⁴He mixtures with molar concentrations of ³He of 0.12, 0.20 and 0.45 under saturated vapor pressure. λ-anomaly was clearly observed in the temperature dependence of T₁.     

The superfluid fraction near Tλ in dilute solutions of 3He in 4He

Existing second-sound velocity measurements are interpreted to imply an unexpectedly strong concentration dependence for the amplitude of $\text{?}{}_{\mathrm{s}}\text{?}$.     

Hydrodynamic parameters and correlation functions of superfluid 3He

In this paper we present the first of two closely related studies devoted to the connection between the phenomenological hydrodynamics and microscopic theories of superfluid ³He. In this first part, we express in a systematical way all the phenomenological parameters appearing in the hydrodynamic equations in terms of microscopically well defined correlation functions. The method used for this purpose goes back to the work of Kadanoff and Martin on normal fluids and has recently been formulated in the framework of Mori's projector formalism by Forster. Apart from the assumptions about the structure of the superfluid phases of ³He and certain regularity assumptions about the collision-dominated part of the correlation functions, which have to be satisfied if the hydrodynamic limit exists at all, but which remain unproven, this part of our work is nearly exact. The only approximation made is the perturbative treatment of the very small magnetic dipole energy. The k → O limit of various correlation functions is considered. Novel consequences of the directional long range order for the transverse momentum density correlation function of the A phase, which are unique to that phase, are obtained. The instantaneous reactive parameters of the system are expressed as equal time commutators and evaluated rigorously. Some reactive parameters, e.g. the one leading to “orbit waves” are shown to have a collisional part, which has not yet been evaluated in a microscopic theory. NMR is considered as the k → O limit of spin wave resonances with an energy gap due to the magnetic dipole-dipole interaction at k = 0. The NMR linewidth is thereby fixed by the same transport parameter, which determines the spin wave damping in the theory where the gap is neglected. The relevant transport parameter is expressed along with all others by the rigorous Kubo formulae of the theory in which the magnetic dipole energy is neglected. The close analogy of the NMR linewidth parameter to transport parameters like the shear viscosity, which are measured in quite different experiments, is thereby elucidated. Further, approximate evaluations of the Kubo relations of these parameters, within a common microscopic approach will be given in a second related study.     

High temperature spontaneous ferromagnetism and other magnetic phenomena in liquid 3He and 3He4He dilute mixtures

Equilibrium ferromagnetic ordering in liquid ³He at temperatures T ? 0.3 K due to long-wavelength spin fluctuations is predicted. The magnetocaloric effect and other thermodynamic properties of ³He↑ are discussed. The properties of ³He↑⁴He solutions are considered in the case of a restricted geometry.     

Separable interactions and liquid 3He

A rigorous expression is given for the free energy of a system of fermions in the presence of a magnetic field interacting via a pairing hamiltonian in the weak-coupling limit. Starting from this expression Landau expansions are derived in two special cases, i.e. the case of general l-wave pairing in zero field and the case of l = 1 pairing, which applies to liquid ³He, in non-zero field.     

Thermal relaxation in liquid 3He/4He mixtures near the tricritical point

Very long relaxation times τ were observed in our earlier specific heat measurements on liquid ³He/⁴He mixtures in two-phase-states near the tricritical temperature T_O. It appear that 1/τ ∝ (T_O ? T).     

Lifetime of electrons on the liquid surface of superfluid 4He

The lifetime of electrons deposited on the liquid surface of ⁴He was measured. It is smaller than 8 μs at 0.5 K and, as is concluded from its temperature dependence, governed by the electronic mobility parallel to the superfluid surface.