Critical current for the flow of superfluid3He in a confined geometry

We determine in a simple model the depression of the critical current in the B phase of superfluid³He due to the presence of boundaries. Results are given for a parallel-plate and a cylindrical geometry, using both analytical and numerical solutions to the Ginzburg-Landau equations.     

Dimensionality crossover of the4He superfluid transition in a slab geometry

The superfluid density of liquid⁴He is computed from vortex renormalization theories for the case of a slab geometry with a slab height L. With increasing temperature there is a crossover from three dimensions to two as the size of the largest vortex rings approaches L and they intersect with the walls, forming vortex pairs. The superfluid density becomes anisotropic, with the component parallel to the slab undergoing the universal Kosterlitz-Thouless jump, while the perpendicular component remains finite. The results are in agreement with both finite-size scaling and Monte-Carlo simulations.     

Quasiclassical Green's function in slab geometry: Application to A-B transition of superfluid3He in a slab

We show that the quasiclassical Green's function method can be used in slab geometries when the separation is much longer than the Fermi wavelength; consequently, quantum interference effects due to the double walls can be averaged out. We apply the quasiclassical method to the A-B transition of superfluid³He in a slab with specular walls at arbitrary temperature. We consider the phase transition between the planar state and the BW state within the weak coupling theory. The phase transition is shown to be of second kind at all temperatures. We obtain the critical size at which the B phase becomes unstable as a function of temperature. AtT=0 K and at SVP, the critical size is estimated to be 0.78 µm.     

Depressions of superfluid density and transition temperature of3he confined in small pores

Using fourth-sound techniques, the superfluid density of³He confined in three separately packed alumina powders having volume-averaged pore radius equal to 1.9, 0.44, and 0.18 µm were measured as a function of temperature at 10 pressures between 11 and 31 bar. Systematically larger depressions of superfluid density were observed as the pore size decreased. The measured pressure dependence of the depression of the superfluid transition temperature is consistent with that of the BCS expression for the coherence length. The quality factor of fourth-sound resonance was measured as a function of temperature at 20.5 and 30.9 bar. The highest quality factor measured was 40. The temperature dependence of the quality factor is in qualitative agreement with a theory by Jensen et al.     

Dislocation dynamics in confined geometry

A simulation of dislocation dynamics has been used to calculate the critical stress for a threading dislocation moving in a confined geometry. The optimum conditions for conducting simulations in systems of various sizes, down to the nanometer range, are defined. The results are critically compared with the available theoretical and numerical estimates for the problem of dislocation motion in capped layers. This revised version was published online in July 2006 with corrections to the Cover Date.     

Spin dynamics of superfluid3He-B in a slab geometry

The spin dynamics and the spin relaxation mechanisms of the superfluid³He-B were studied by using the NMR method in a slab geometry, where the superfluid3He-B was confined between narrow parallel plates with a gap smaller than the healing length of then-texture and the magnetic field was applied parallel to the plates. The relaxation parameter in the Leggett-Takagi (LT) equations was determined from a line width measurement of the transverse CW NMR. By using the pulsed NMR method, spin dynamics were studied in the nonlinear region. The observed spin dynamics were in good agreement with a numerical calculation of the LT equations together with the relaxation parameter determined by the CW NMR. When the tipping angle became larger than a certain critical value, the superfluid³He-B entered the Brinkman-Smith (BS) state. In this case, we observed the slow relaxation process in the BS state and then the rapid recovery process from the BS state to the initial non-Leggett configuration. The slow process in the BS state was attributed to the surface relaxation mechanism due to the torque from the surface-field energy.     

Depression of the superfluid transition in4He

We study superfluid⁴He near T in a homogeneous metastable state where a finite superfluid velocity v_s is present. Neglecting vortices we perform a renormalization-group calculation of the critical velocity v_sc(T) at which the superfluid state becomes unstable. We apply this result to the situation where the superfluid velocity is induced by a finite heat current Q. A critical heat current Q_c(T) corresponding to v_sc(T) is found which implies a transition temperature T (Q)=T[1–A_oQ^x]. We determine the exact exponent x=[(d–1)v] ^–1 0.744 in d=3 dimensions and calculate A_o in one-loop order. Our results for A_o and x are compared with recent experimental data.     

Surface tension anomaly at the superfluid transition

A simple scaling argument is given to estimate the anomaly in surface tension at the -point of liquid helium. The result agrees with an earlier one of Sobyanin, based on the Ginzburg-Pitaevskii equation.     

Magnetic dissipation in superfluid3He-B in the transition regime to nonhydrodynamic conditions

We have applied the so-called HPD spectroscopy, i.e. the NMR of the homogeneously precessing domain (HPD) in superfluid³He-B, to study the magnetic relaxation processes down to 0.3T _c . The power absorbed by HPD from cw NMR rf-field was divided into several contributions corresponding to different relaxation processes. From these contributions nonhydrodynamic corrections to spin diffusion and Leggett-Takagi (L-T) relaxation were extracted for a pressure of 6 bar. Below 0.45T _c a large absorption term linear with the HPD length and increasing with the falling temperature was observed. This term could be associated with an instability of coherent precession in the nonhydrodynamic regime. The process of the HPD formation in the nonwetting regime, forT<0.37T _c , was observed and described, leading to a new possibility to determine thed-constant of the surface energy.     

Fluctuations above the superfluid transition in liquid3He

It is shown that fluctuations above the superfluid transition in liquid³He depend strongly upon the relative angular momentum1 for which Cooper pairing occurs. The effects may be calculated for any value of1 and they should be observable in the static magnetization, viscosity, and spin diffusion coefficient, giving a means of determining1. Conclusions to be drawn from existing experiments are discussed.Work supported by Energy Research and Development Administration.     

He I-He II coexistence near the superfluid transition

We have made a numerical scheme of solving two fluid hydrodynamics near the point, which includes the mass density, momentum density, entropy density, and complex order parameter. In our model the normal fluid velocity vanishes at the boundaries due to finite viscosity. As preliminary examples we examine coexistence of a superfluid region and a normal fluid region in two space dimensions firstly in heat flow and secondly in gravity and heat flow. We observe formation of a vortex from a wall in the second case.     

The superfluid transition of a helium film according to the Landau-Ginzburg-Pitaevskii theory of helium II

The superfluid transition of a helium film is discussed in the framework of the phenomenological Landau-Ginzburg-Pitaevskii theory. In order to obtain agreement with experiments, it turns out to be essential to check the film solutions of the Ginzburg-Pitaevskii differential equation for stability.     

Planning of an experiment to investigate the evaporation of a film of hydrocarbon fuel

A method and results of a multifactor experiment to investigate the rate of evaporation of a film of fuel in a flow of air are presented.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 38, No. 2, pp. 325–328, February, 1980.     

Critical heat flow in a thick He II film near the superfluid transition

Measurements of critical heat flow in a thick He II film near the onset temperatureT ₀are presented. Estimates of the film thickness were made by comparison with the critical velocity for bulk helium in pores, and from the onset temperature for superfluidity. These comparisons yield a thickness of 2.5×10^–5 and 2×10^–5 cm, respectively. The observed critical heat flow, in conjunction with reasonable estimates of the superfluid density, yields a critical velocityv _sc ^* that has the same temperature dependence as the critical velocityv _scobtained by Clow and Reppy from gyroscopic measurements. The present results are consistent with the idea that there is a region nearT ₀wherev _sc ^* =v_{sc s} and it is independent of geometry, and a geometry-dependent region well belowT ₀wherev _sc ^* =v_sc constant. Available data on the depression of the onset temperature are examined. Although they are consistent with recent phenomenological calculations, they are not sufficiently accurate to provide conclusive evidence in favor of these theories.     

Dispersion corrections to the collective mode spectrum in axial and planar phases of superfluid He3

Using the path integration technique developed by Brusov and Popov earlier, we have calculated for the first time the dispersion corrections to the collective mode spectrum in A- and 2D- phases of superfluidHe ³ for arbitrary directions of the collective excitation momentumk, taking the damping of collective modes into account. In axial-phase clapping (cl) mode remains six fold degenerate fork l, while for other directions a three fold splitting takes place, which reaches a maximum fork l. The pairbreaking modes remain degenerate even taking the dispersion induced corrections into account. In the planar phase the degeneracy of clapping (cl) and quasi-Goldstone (qGd) modes depends on the direction of the collective mode momentumk with respect to the external magnetic fieldH: the mode degeneracy remains the same as in the case of zero momentumk fork H only, and for any other directions two fold splitting of these modes takes place. The dispersion induced splitting of collective modes could be observed (at least in the A-phase) in sound absorption experiments.     

The superfluid fraction of3He confined in pores of sintered silver

We have measured the superfluid fraction of³He confined within the pores of silver sinter. Four sintered substrates were prepared with packing fractions between 23% and 68% of solid density. Measurements were carried out at six pressures between 0 bar and 29 bar. These results show that the superfluid fraction is suppressed to a much greater extent than expected.     

Nuclear magnetic resonance of3He superfluid confined in high porosity aerogel

We report pulsed nuclear magnetic resonance (NMR) measurements of the transverse frequency and magnetization of³ He confined in aerogel with 98.2% open volume porosity. A homogeneous superfluid phase is observed at pressures, P > 12 bar, accompanied by a sharp onset of frequency shifts showing little or no textural broadening; a result quite unexpected for³He confined in random porous media. The transition temperatures and order parameter are both significantly suppressed from their bulk values and the magnetization data indicate this low temperature phase is an equal-spin pairing superfluid. For NMR tipping angles greater than 40 ° the resonance frequency drops abruptly to the normal state value. This tip angle dependence is not consistent with either the bulk³He-A or³He-B superfluid phases.     

Mutual friction and vortex motion near the superfluid transition

The mutual friction parametersB and B for a moving vortex are calculated near the superfluid transition. They are proportional to the kinetic coefficient associated with the order parameter and, asT , diverge as (T – T)^–1/3, in agreement with experiment. The nonlinear couplings between the order parameter and the entropym, both the reversible one and the one in the free energy, are found to be crucial in the mutual friction near the point. These couplings were neglected in a previous paper by the author. First, the reversible coupling in the dynamic equations makes the chemical potential deviation long-ranged and causes the dissipation to take place only near the vortex core. Second,B can diverge asT T only in the presence of the coupling of the formm||² in the free energy. Thus theE model of Halperin et al., where the latter coupling is absent, cannot explain the critical anomaly ofB. The helical mode of a single vertex line is also investigated and its dispersion relation is found to be quite different from that at low temperatures. This mode has the same time scale as that of the second-sound mode when the wave vectors are of the order of the inverse correlation length, thus obeying the usual dynamic scaling law. The time correlation functions of the displacement fluctuations of a vortex line are also obtained. The force acting on a moving vortex is calculated and is found to be equal to the classical Magnus force.