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.     

Transverse zero sound propagation in superfluid 3He

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

Static susceptibility and longitudinal resonance frequency of superfluid 3He B

The static susceptibility and the longitudinal resonance frequency of superfluid ³He B have been measured at 18.7 bar from T_c to 0.27 T_c using continuous wave transverse NMR.     

Transverse and longitudinal nuclear magnetic resonance in superfluid <Superscript>3</Superscript>He in anisotropic aerogel

It is found that the properties of nuclear magnetic resonance of both superfluid phases of ³He in an anisotropic aerogel can be described in terms of the bulk superfluid order parameters with the orbital order parameter vector fixed by anisotropy of the aerogel sample. It is also shown that, by proper squeezing, it is possible to attain a sample with isotropic NMR properties.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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 $\text{?}{}_{\mathrm{s}}\text{?}$.     

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.     

On the superfluidity of 3He in dilute mixtures of 3He4He

It is shown on the basis of the experimental data on thermodynamic and transport properties under pressure that the temperatures of the transition of ³He to the superfluid state for ³He-⁴He solutions with concentrations 0.6-3% lie in the range 0.4–1.4 mK.     

Coherent pion production in 3He3He collisions

A model is proposed to describe the near-threshold production of pions in the ${}^3\text{He}\text{(}{}^3\text{He}\text{, π}{}^{\mathrm{+}}\text{)}{}^6\text{Li}$ reaction. Taking experimental data on the ${}^3\text{He}\text{(p, π}{}^{\mathrm{+}}\text{)}{}^4$He process as input the cross sections for the first three levels of ⁶Li are reproduced semi-quantitatively.     

Study of two-phonon excitations in superfluid 4He

We explain the second branch of excitations in superfluid ⁴He observed by Cowley and Woods, by accounting for two-phonon contributions to the dynamic structure function, S(k, ω). Our theory gives a good fit with the experimental data in the high energy region for several values of momentum transfer. It is observed that the contribution to S(k, ω) due to two-phonon excitations is of the order of k² as against its k⁴ dependence reported in earlier theories.     

On the application of spin-fluctuation theory to superfluid 3He

Spin-fluctuation theory, modified to include non-paramagnon effects, is shown to be capable of yielding quantitative results for the pairing interaction and the Anderson-Brinkman parameter δ in a natural manner.