Experimental and Theoretical Problems of the Quantum Phase-Separation Kinetics of Liquid 3He-4He Mixtures

The nucleation of the ³ He-concentrated phase is analyzed at the phase-separation of a supersaturated liquid ³ He– ⁴ He mixture in a wide range of temperatures. The crossover from the classical kinetics to the quantum kinetics is considered. Besides the homogeneous bulk nucleation the nucleation under heterogeneous conditions due to the possible presence of quantized vortices is examined.     

Observation of Anomalously Low Momentum Transfer in the Low Energy Scattering of Large 4He Droplets From 4He and 3He Atoms

The momentum transferred to large superfluid ⁴ He droplets in low energy ( 4–10 K) scattering from ⁴ He and ³ He atoms was determined from time of flight measurements after the droplets have passed through a low temperature (T = 1.7–4.2 K) scattering box filled with the gas of either He isotope. The results are compared with ³ He droplets scattered from either ⁴ He or ³ He gas for which all of the incident momentum is transferred, as expected for classical capture of the scattering gas atoms. In the case of the ⁴ He droplets a smaller momentum transfer is found amounting to 65% for ⁴ He atoms and 45% for ³ He atoms but only at the lowest collision energies. These results are consistent with transmission of some of the atoms through the droplets.     

Pinning of Quantized Vortices in Mixed 3He-4He Droplets

We use density functional theory to investigate the structure of mixed ³ He _{N 3} – ⁴ He _{N 4} droplets with an embedded Xe atom that pins a quantized vortex line. While ³ He atoms are distributed along the vortex line and on the surface of the ⁴ He drop, the impurity is mostly coated by ⁴ He atoms. Results for N ₄ =500 and a number of ³ He atoms up to N ₃ =100 are presented, and the binding energy of the dopant to the vortex line is determined.     

Percolative diffusion of dissolved3He atoms in He II through porous media

The diffusion of³He quasiparticles in a dilute³He-⁴He solution confined in the porous medium is discussed on the basis of the percolation theory. It is pointed out that when³He quasiparticles diffuse through the porous medium,³He quasiparticles feel the random potentials originating from the random distribution of channel radii connecting pores. Noticing that the³He concentration can be varied over a wide range in³He-⁴He solutions, we find that the chemical potential of³He quasiparticles is related to the bond percolation densityp of the porous medium. It is emphasized that the mobility edge for³He quasiparticles is different between up and down spins under high magnetic fields. A novel mechanism utilizing this characteristics is proposed to produce the degenerate Fermi system with a very high polarization ratio. A discussion is given of the spatial localization of dissolved³He atoms due to the quantum interference. It is suggested that the localization effect is realized by the NMR experiments at very low temperatures.     

Decay of 2 - Anions in Solid Parahydrogen via Two-Stage Quantum Tunneling Diffusion Processes

Decay mechanism of H ₂ ^- anions in X()-irradiated solid para-H₂ (p-H ₂ ) has been studied using high-resolution ESR spectroscopy in the temperature range between 1.3–6.6 K. The results are summarized as follows. First,the decay rate constant of the ₂ ^- anions is not proportional to initial yields of reactive species such as cations and H atoms but proportional to the concentration of less-reactive species of HD molecules in p-H₂ . This result shows that the decay of the ₂ ^- anion is due to the reaction neither with cations nor H atoms but with HD molecules originally contained in the p-H₂ sample at natural abundance. Second,the decay rate constant of the ₂ ^- anions increases proportionally with the increase in temperature below 3 K and decreases with the increase in temperature between 3–5 K,although it increases exponentially with the increase in temperature above 5 K. This result indicates that the decay rate constant of the ₂ ^- anions is controlled by the rate constant for the diffusion of the ₂ ^- anions via one-phonon assisted quantum tunneling below 3 K,two-phonon scattered or assisted quantum tunneling between 3–5 K,and thermally-activated process above 5 K.     

Baryon Asymmetry of Universe: View from Superfluid 3He

The origin of the excess of matter over antimatter in our Universe remains one of the fundamental problems. Dynamical baryogenesis in the process of the broken symmetry electroweak transition in the expanding Universe is the widely discussed model where the baryonic asymmetry is induced by the quantum chiral anomaly. We discuss the modelling of this phenomenon in superfluid ³ He and superconductors where the chiral anomaly is realized in the presence of quantized vortex, which introduces nodes into the energy spectrum of the fermionic quasiparticles. The spectral flow of fermions through the nodes during the vortex motion leads to the creation of fermionic charge from the superfluid vacuum and to transfer of the superfluid linear momentum into the heat bath, thus producing an extra force on the vortex, which in some cases compensates the Magnus force. This spectral-flow force was calculated 20 years ago by Kopnin and Kravtsov for s-wave superconductors, but only recently was it measured in a broad temperature range in Manchester experiments on rotating superfluid ³ He. The momentogenesis observed in ³ He is analogous to the dynamical production of baryons by cosmic strings. Some other possible scenaria of baryogenesis related to superfluid ³ He are discussed.     

Phase Separation Kinetics of Solid 3He-4He Mixtures

The kinetics of isotopic phase separation in solid mixture of ³ He in ⁴ He with the initial concentration 2.05 % at various molar volumes has been investigated by precise pressure measurements. It has been shown that during both stepped and fast cooldown into the metastable region the equilibrium of coexisting phases is described by the exponential law with a characteristic time constant , The value of is found to decrease as the molar volume increases and the temperature lowers. It confirms that the growth of the ³ He-rich phase is connected with nonthermally activated (quantum) diffusion in the gas of delocalized ³ He quasiparticles. The obtained experimental results can be described only qualitatively by current kinetic theory of binary quantum solid mixtures. The conditions permitting the realization of the isotopic phase separation during the time observed in the experiment are analyzed. The effective quantum diffusion coefficient providing required ³ He atoms transport is about an order of magnitude higher than the corresponding value measured in NMR experiments. These conditions are probably fulfilled at the big concentration gradient which takes place at isotopic phase separation. The corresponding kinetic theory should be developed.     

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 .     

Interfacial Tension of Phase-Separated 3He-4He Mixtures under Pressure

We measured the interfacial tension of ³ He-⁴ He mixtures under pressure of 21 atm down to about 0.2K by using the resonance of the interfacial wave and found that the decrease from absolute zero is proportional to T² up to about 0.4 K. From the simple extrapolation of this T²-dependence the interfacial tension at absolute zero is obtained as _i (0) = 19.3 ± 1.3 mdyne/cm. Compared with saturated vapor pressure, the interfacial tension at absolute zero decreases by about 20%, and the coefficient of the T²-dependence does not depend strongly on pressure. The large T²-dependence both at saturated vapor pressure and at 21 atm may be attributable to the change in density difference between the two phases.     

Superfluid 3He Simulation of Cosmic String Creation in the Early Universe

We discuss the first experimental observations of a deficit in the thermal energy released after the exothermic neutron-³ He nuclear reaction in superfluid ³ He at temperatures approaching 100K. We propose that this deficit is associated with the creation of a vortex tangle as the liquid ³ He recrosses the superfluid transition. This process has many similarities with the theory of cosmic string creation during the GUT and electroweak transitions shortly after the Big Bang. Our measurements constitute the first quantitative test of defect creation via the cosmological Kibble mechanism for gauge symmetry breaking phase transitions and agree very well with the predictions of Zurek's scenario.     

Surface Effects of 4He Coating on the Viscosity and the Slip Length of Normal and Superfluid 3He

We have measured the viscosity, , and the slip length, , of normal and superfluid ³ He using a torsional oscillator with a thick sample space. We coated the oscillating surface with 2.5 layers of ⁴ He film to study how the ⁴ He thin film changes the scattering mechanism of ³ He quasiparticles at the cell wall at 5 bar and 21 bar. In the normal phase, the temperature dependence of the viscosity was changed a little by the ⁴ He film at 21 bar but no change was observed at 5 bar. The slip length was enhanced by ⁴ He coating at 5 bar. This enhancement indicates the increase of specularity of ³ He quasiparticles scattering at the oscillating surface. On the other hand, a reduction of the slip length was observed at 21 bar. In the superfluid phase, the temperature dependence of supports the existence of Andreev reflection even with ⁴ He film on the surface at 5 bar and 21 bar.     

Studies of 2D Cryocrystals by STM Techniques

Scanning tunneling microscopy (STM) studies of two-dimensional (2D) cryocrystals ⁴ He, Kr, Xe) physisorbed on graphite surfaces are presented. Individual helium atoms, usually thought to be invisible with STM, were recently observed on graphite surfaces at a density corresponding to the commensurate solid. Here we show that a local elastic deformation seems to be the principal mechanism responsible to render the atoms visible. Recent tight-binding calculations of the local density of states (LDOS) of graphite which predict the appearance of an energy gap support this picture. I-z curve measurements for the case of ⁴ He show a sharp drop (increase) of the tunneling current I at a certain tip-surface distance z during retraction (approach) of the tip. This drop (increase) may be associated with the tunneling of a single He adatom, opening new possibilities to study the quantum tunneling of atoms via STM.     

3He Transverse Excited State Occupation in Thin 3He-4He Films

The discovery that ³ He was occupying transverse excited states at submonolayer coverages in ³ He-⁴ He mixture films on a Nuclepore substrate, was a surprise. In this note we discuss the relationship between theory and experiment in attempting to understand the physics of this behavior. We first discuss various single-atom-limit calculations of the level spacing between the ground-state and first excited state. We then introduce a free, quasi-particle picture for analyzing experimental magnetization step data and compare those results with the single-atom-limit calculations. The experiments clearly show excited state occupation at submonolayer coverages in contradistinction with the calculations. We then briefly discuss a microscopic, semi-phenomenological theory which, in agreement with experiment, yields ³ He occupation of the first excited state at submonolayer coverages. The mechanism is a model ³ He-³ He effective interaction due to one ripplon exchange. This effective interaction is density dependent and very long ranged. It strongly modifies the small-k properties of the ³ He self-energy and, in particular, causes the ground-state to first excited state level spacing to decrease with increasing ³ He areal density.     

The dielectric formalism for3He-4He mixtures

The microscopic theory of³He-⁴He mixtures with a Bose condensate is formulated in terms of the dielectric formalism. By expressing all correlation functions in terms of proper, irreducible contributions, one sets the stage for approximate calculations that will be consistent with various exact sum rules and Ward identities, just as in the case of pure⁴He. The present analysis includes a symmetry-breaking term that allows us to deal with the continuity equations properly, and is valid at finite temperature. As a specific application, we express the normal fluid density _N in terms of the static⁴He current-current correlation function. We also give the first formal proof that in the presence of a moving condensate, the³He atoms make no direct contribution to the superfluid flow.     

Transverse relaxation in two-level Fermi liquids and gases

An exact microscopic theory is developed for transverse dynamics in two-level Fermi systems like spin-polarized Fermi liquids. The origin of a transverse zero-temperature attenuation is a dephasing of interlevel transitions in inhomogeneous conditions. We analyze different sources of this relaxation using an extrapolation from low polarizations or densities. These sources include imaginary terms in the vertex and single-particles' energies and pseudo-energies away from the Fermi spheres, and derivatives of the vertex function in off-shell directions. The attenuation for dilute systems starts from a second order term in density. The main non-local contribution is of the next order in density, but is not negligible if the interaction range is large. At very low polarizations and densities, one recovers the already known results. The implications for liquid³He and³He-⁴He mixtures are discussed.     

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.     

Monte Carlo calculation of exchange in solid3He

A Monte Carlo calculation of theT=0 nearest-neighbor exchange frequencyJ is used to show that the short-range correlations between an exchanging pair of atoms and their surrounding neighbors are of considerable importance to the exchange process in solid ³ He. Their effect onJ is to steepen its density dependence, and decrease its magnitude. The calculation was prompted by the neglect of these many-body correlations in recent theories.Work supported in part by the U.S. Atomic Energy Commission under Contract No. AT(11-1)-1569.Based in part on the Ph.D. thesis of A. K. McMahan, University of Minnesota, 1971, unpublished.     

The transverse acoustic impedance of dilute solutions of3He in superfluid4He

The transverse acoustic impedanceZ=R–iX of dilute solutions of³He in superfluid⁴He has been measured at a frequency (/2) of 20.5 MHz at temperaturesT from 30 mK to the transition at T. The³He concentrations studied werec=0.014, 0.031, 0.053, 0.060, and 0.092 below 1 K, thoughc decreased slightly near the point. The impedance was found from the temperature dependence of the quality factor and the resonant frequency of anAT-cut quartz crystal resonator immersed in the liquid. Below 1 K,Z is due to the Fermi gas of³He quasiparticles, and in the collisionless limit, 1 ( is a relaxation time),R remains constant whileX goes to zero. Measurements ofR(c, T) andX(c, T) were analyzed to determine the momentum accommodation coefficient (c, T) and (c, T). The relaxation times were in good agreement with previous work, while (c, T) was independent ofc, but increased from 0.29±0.03 below 0.1 K to 1.0±0.1 above 0.8 K. Various mechanisms are suggested to explain this. Between 1.0 and 1.5 K the³He quasiparticles and the thermally excited rotons are in the hydrodynamic region, 1. Values of the total viscosity (c, T) were obtained and analyzed to give the³He gas viscosity and the³He-³He and roton-³He scattering rates, both of which were energy-dependent. The superfluid healing length a was also measured. Near the point we founda=(0.1±0.03)^–2/3 nm, where =1–T/T, proportional to the phase coherence length . Our data are consistent with the hypothesis that _s/T is a universal constant for superfluid dilute solutions, where _s is the superfluid density. Between 1.0 and 1.8 K we found thata(c, T) was comparable to measurements in³He-⁴He films.     

Zero-temperature attenuation and transverse spin dynamics in fermi liquids. III. Low spin polarizations

This is the third in a series of papers on microscopic theory of transverse dynamics in spin-polarized Fermi liquids. In the lowest order in polarization our exact general theory of Ref. 1 reproduces the conventional Landau-Silin-Leggett theory of Fermi liquids. The next term in polarization expansion contains a zero-temperature attenuation with the magnitude that does not depend on polarization. This attenuation results in a finite relaxation time in transverse spin dynamics at zero temperature and is responsible for anomalous temperature behavior of spin diffusion. The zero-temperature attenuation is determined by two angular harmonics of the derivatives of the mass operators and the irreducible vertex in off-shell directions, and cannot be expressed via standard Fermi liquid harmonics. At high polarizations, the parameters of transverse spin dynamics are calculated as an expansion in polarization. The expansion involves complex values of interaction function and energy on a set of isoenergetic surfaces with the radii between the Fermi momenta for up and down spins,p andp. The results explain recent experimental data on spin diffusion in spin-polarized liquid³He and³He-⁴He mixtures. The comparison with experimental data indicates that the superfluid transition temperature for³He in³He-⁴He mixtures may be much lower than the current estimates.     

Sound and transport phenomena in spin-polarized3He-4He solutions

Transport phenomena in partially spin-polarized³He-⁴He solutions are investigated. The polarization causes considerable changes in kinetic coefficients and also gives rise to new dissipative processes, such as spin thermodiffusion and second viscosity. The transport coefficients are calculated for degenerate and nondegenerate³He-⁴He solutions. The absorption of first- and second-sound waves is studied. Second-sound propagation is affected by weak dipole interactions and its velocity depends significantly on the frequency.