Showing papers in "Journal of Low Temperature Physics in 1982"

On a quasiclassical Langevin equation

Abstract: It is shown that the motion of a quantum mechanical particle coupled to a dissipative environment can be described by a Langevin equation where the stochastic force is generalized such that its power spectrum is in accordance with the fluctuation-dissipation theorem. This generalized Langevin equation has an interesting range of applicability. It includes the quasiclassical regime provided that the damping, that is, the coupling of the particle to its environment, is sufficiently strong.

Photographic Studies of Quantized Vortex Lines

Abstract: A study of the behavior of systems of quantized vortex lines in rotating superfluid4He is described. Using a photographic technique, the positions of the vortex cores at the free surface of the liquid are recorded in the form of time-lapse motion pictures. The observation of stationary arrays of vortices are discussed and a comparison with the predictions of rectilinear vortex theory is made. Discrepancies between the observations and this theoretical model are noted, and the limitations of the experimental method are described. Several distinct types of periodic array motion have been observed. A description of their analysis as well as possible theoretical and experimental interpretations are given. The final part of this study involves phenomena associated with acceleration of the vessel. The analysis of film records and light signal amplitude measurements for repeated spinups of the vessel reveals statistical trends in the rate of appearance of vortices.

Comment on: ''DC SQUID: Noise and Optimization'' by Tesche and Clarke

Abstract: Due to a numerical error, the computed noise energy of a dc SQUID, neglecting capacitance, as given by Tesche and Clarke is too small by a factor of about two.

The density distribution of a weakly interacting bose gas in an external potential

Abstract: The Gross-Pitaevskii equations are generalized to finite temperatures by means of the self-consistent Hartree-Fock and Bogolyubov approximations that are derived through a variational principle for the optimal set of one-particle eigenstates. A number of sample density profiles are provided for spin-polarized atomic hydrogen when the external potential depends on thez coordinate only

On the theory of superfluidity of helium II near the λ point

Abstract: The present state of the Ψ theory of superfluidity of helium II near the λ point is reviewed. The basic assumptions underlying this theory and the limits of its applicability are discussed. The results of the solution of some problems in the framework of the theory are presented and compared with experimental data. The necessity and possibility of further comparison of the theory with experiment are emphasized.

3He-melting-curve thermometry

Abstract: Precise measurements of theP-T relation along the melting curve of3He have been made for 8≲T≲330 mK. The results are in excellent agreement with other precise data for temperatures near the extremes of this range. A best-fit relation is provided which describes the melting curve to within ±1 mbar between the superfluid A transition and the pressure minimum. Detailed descriptions of the melting curve and magnetic thermometers used for the calibration are also given.

Anomalous temperature dependence ofD andT2 for dilute solutions of3He in solid4He

Abstract: Results of measurements of the spin diffusion coefficientD and NMR relaxation timesT1,T2, and T1p are presented for a range of fractional3He concentrations 1 × 10−4≤x3≤2.5 × 10−3 in solid4He at molar volumes 19.85≤Vm≤21.0 cm3 and temperatures 0.4

Analysis of a double-loop dc SQUID

Abstract: An analysis of a double-loop dc SQUID is performed. The device consists of a superconducting loop containing two nonhysteretic Josephson junctions connected in series with a resonantL-C circuit. A lumped-circuit-element model for the device is described. Noise-free current-voltage characteristics are computed as a function of the device parameters. Multivalued and hysteretic characteristics are observed. Noise rounded characteristics, flux-to-voltage forward transfer functions, and low-frequency voltage and circulating current noise spectral densities are computed by numerical simulation. The optimal flux resolution is shown to be limited by hysteresis in the I-\(\bar V\) characteristics to a value comparable to a conventional dc SQUID with the same total loop inductance. The double-loop structure permits the use of dc SQUID geometries with enhanced coupling properties without loss of sensitivity.

Magnetic field dependence of the Leggett angle, the susceptibility, and the longitudinal nuclear magnetic resonance of3He-B

Abstract: The magnetic field dependences of the Leggett angle, the susceptibility, the free energy, and the longitudinal NMR frequency of3He-B are calculated from a generalized weak coupling theory. Employing the experimental values for the Landau parametersF0a andF2a, reasonable agreement with the susceptibility data measured recently by Hoyt, Scholz, and Edwards is obtained. Substantial field dependence of the Leggett angle and the longitudinal NMR frequency is predicted.

Kapitza resistance between liquid and solid helium. I. Theory

Abstract: Detailed calculations are presented of the phonon transmission between liquid and solid helium. The transmission coefficients are used to determine the Kapitza conductance. Calculations have been made based on the usual acoustic-mismatch theory, and also using a modified theory in which it is assumed that very rapid melting and freezing can occur at the interface.

Energy dependence of the effective mass in liquid3He

Abstract: The striking behavior of the specific heat of liquid3He as function of temperature at low temperatures requires the effective massm* to change rapidly with temperature; this can be translated into a rapid variation with energy,m*/m dropping from itsE=0 value to ∼1 over the temperature range ≲0.5 K. We explore this effect in a model in which the enhancement of the effective mass is due to coupling to spin fluctuations. At very lowT≲50 mK, the variation in specific heat results fromT3 lnT terms. The free energy, on the other hand, does not containT2 lnT terms in its dependence on the magnetic field, implying that the susceptibility, which is essentiallym*/(1+F0a), also does not have such logarithmic terms. Consequently, ifm* varies with energy, so mustF0a, so as to leave the susceptibility free of this rapid variation. The rough constancy ofm*/(1+F0a) seems empirically to hold to higher energies and temperatures. Ifm*/m drops, with increasing energy, to unity, the spin-fluctuation theory, which is described in terms of Landau parameters at the Fermi surface, goes over into the paramagnon theory. The rapid change with energy of the effective interactions can be understood within the framework of response theory as a “shaking off” of the relevant collective modes with increasing frequency of the imposed oscillations. The changes in effective interactions have consequences for the interpretation of experiments involving inelastic neutron scattering from liquid3He.

Transport properties of helium near the liquid-vapor critical point. I. Thermal conductivity of 3 He

Abstract: A study of the thermal conductivity λ of3He is reported along several isotherms above the critical point and along the critical isochore. After a detailed description of the apparatus and the measurement procedures, the conductivity results away from the critical region are presented and compared with those of Kerrisk and Keller. Using the assumption that λ can be decomposed into a singular part λsing and a background contribution, λsing is analyzed in terms of the scaling theory. The critical exponent for λsing, ψ=0.57, is in good agreement with the predicted one. Departures from a simple power law very close toT c are discussed. There is no evidence for convective enhancement of λ. It is also found that λsing scales like (ρ2 k T )1/2, as proposed by Sengers. Here ρ andk T are the density and compressibility. The thermal diffusivityD T =λ/ρC p , whereC p is the specific heat, is compared with the results obtained from the Rayleigh linewidth of scattered light, and a systematic discrepancy in amplitude is found that remains unexplained. Furthermore, the relaxation times τ for reaching the steady state after switching the heat flux on and off are reported along the critical isochore and are compared with calculations using the steady state results for the thermal diffusivity.

Rf SQUID in the nonhysteretic regime with k 2 Ql>1

Abstract: Experimental measurements of current-voltage, current-phase, amplitude-frequency, phase-frequency, and signal characteristics of an rf SQUID operating at a frequency of 30 MHz in the nonhysteretic regime (1 = 2..pi..L/sub 0/I/sub 0//phi/sub o/ 1. Here I/sub 0/ is the critical current of the weak link, L/sub 0/ is the SQUID ring inductance, k is the coefficient of coupling of the SQUID ring to a resonant tank circuit of quality Q, and phi/sub 0/ is the magnetic flux quantum. A numerical analysis of the above characteristics for all relevant parameter values close to those occurring under experimental conditions was performed for qualitative comparison with theory. The main difference from the traditional nonhysteretic regime of SQUID operation (k/sup 2/Q1 1.« less

Very low-temperature search for superconductivity in semiconducting KTaO 3

Abstract: A series of attempts have been made to detect the presence of superconductivity in semiconducting potassium tantalate (KTaO3) single crystals. Semiconducting potassium tantalate has a number of properties in common with semiconducting SrTiO3, which is superconducting below ∼0.3 K, with a critical temperatureT c that varies as a function of the carrier concentration. Both KTaO3 and SrTiO3 are perovskite-structure oxides and both materials are so-called incipient ferroelectrics that are characterized by high dielectric constants at low temperature. These common properties suggest that superconductivity might also be observed in semiconducting potassium tantalate. In the temperature ange from 0.01 to 4.0 K, however, no evidence was found for superconductivity in KTaO3 in the presence of magnetic fields of 10−5–10−4 T (i.e., 0.1–1 Oe). Below 1.5 K, the search for superconductivity in KTaO3 was carried out using a3He-4He dilution refrigerator equipped with a SQUID magnetometer and an ac magnetometer. The system response was verified by measuring the paramagnetic susceptibility of Dy2O3-doped KTaO3. The failure to observe superconductivity in KTaO3, while SrTiO3 is an established superconducting material, may be related to the fact that the latter substance assumes a tetragonal symmetry phase at 105 K, while KTaO3 remains cubic to low temperatures.

An alternative analysis of the nonlinear equations of the current-driven Josephson junction

Abstract: The current-driven RSJ model is analyzed by considering the phase at the end of one rf cycle as a function of the phase at the beginning. This function has a simple analytic form. An elementary proof of the absence of current steps at subharmonic Josephson voltages is given. Properties of the phaselocked trajectories are discussed which are useful in computing parametric effects.

Response of a superconductor to a supercritical current pulse

Abstract: We investigate the response of a one-dimensional homogeneous superconductor nearT c if a current larger than the maximum supercurrent is suddenly imposed. We determine the time dependence of the order parameter, the voltage, and the quasiparticle distribution function. The delay time between the switching on of the current and the time when the system becomes normal, which is marked by the appearance of a voltage, is determined. Good agreement with experimental results is found.

Critical-field measurements in Nb-Ti composition-modulated alloys

Abstract: We present measurements of the transition temperature and upper parallel critical field, to 15 kG, of layered Nb-Ti alloys for layer wavelengths between 6 and 6250 A.

Low-temperature adsorption of gases on heterogeneous solid surfaces: Effects of surface topography

Abstract: For the adsorption of gases on a solid surface we derive equations for the low-temperature adsorption isotherms, isosteric heats of adsorption, and heat capacities of the adsorbed phase for both a patchwise and a random surface topography. A model of localized monolayer adsorption with nearest neighbor interactions between admolecules is used. The equations are illustrated by appropriate model calculations.

Diffusive relaxation processes in liquid3He-4He mixtures. I. Normal phase

Abstract: When a heat flux is switched on across a fluid binary mixture, steady state conditions for the temperature and mass concentration gradients ∇T and ∇c are reached via a diffusive transient process described by a series of terms “modes” involving characteristic times τ n . These are determined by static and transport properties of the mixture, and by the boundary conditions. We present a complete mathematical solution for the relaxation process in a binary normal liquid layer of heightd and infinite diameter, and discuss in particular the role of the parameterA=k T 2 (∂μ/∂c) T,P /TCP,c coupling the mass and thermal diffusion. HerekT is the thermal diffusion ratio, (∂μ/∂c) T,P −1 is the concentration susceptibility, μ is the chemical potential difference between the components, andCP,c is the specific heat. We present examples of special situations found in relaxation experiments. WhenA is small, the observable times τ(∇T) and τ(∇c) for temperature and concentration equilibration are different, but they tend to the same value asA increases. We present experimental results on four examples of liquid helium of different3He mole fractionX, and discuss these results on the basis of the preceding analysis. In the simple case for pure3He (i.e., in the absence of mass diffusion) we find the observed τ(∇T) to be in good agreement with that calculated from the thermal diffusivity. For all the investigated3He-4He mixtures, we observe τ(∇c) and τ(∇T) to be different whenA is small, a situation occurring at high enough temperatures. AsA increases with decreasingT, they become equal, as predicted. For the mixtures with mole fractionsX(3He)=0.510 and 0.603, we derive the mass diffusionD from the analysis of τ(∇c) and demonstrate that it diverges strongly with an exponent of about 1/3 in the critical region near the superfluid transition. As the tricritical point (Tt,Xt) is approached for the mixtureX=Xt0.675,D tends to zero with an exponent of roughly 0.4. These results are consistent with predictions and also with theD derived from sound attenuation data. We discuss the difficulties of the analysis in the regime close toTλ andTt, with special emphasis on the situation created by the onset of a superfluid film along the wall of the cell forX=0.603 and 0.675.

NMR studies of single crystals of H2. V. NMR anisotropy and order parameter distribution ofX (ortho)≤0.55

Abstract: We report a study of the NMR line shapes in hcp single crystals of H2 with ortho concentrationsX≤0.55 in the regime where there is no longer a transition to a long-range orientationally ordered phase. From the anisotropy of the o-H2 impurity NMR spectrum at low ortho concentration, reached by ortho-para conversion, the crystal orientation is determined. The second momentM2 can be represented by a function of the formM2=Φ(X, T)f(cos θHc), where θHc is the angle between the applied magnetic field and the crystalc axis. For a single crystal, the anisotropy functionf(cos θHc) is found to be independent of temperature and of ortho concentration within experimental error, and is in very good agreement with predictions based on the first term of the high-temperature expansion ofM2 and on other, more general symmetry arguments. An order parameter σ is defined and the distribution functionP(σ) is calculated from the NMR line shapes under the simplifying assumption that the anisotropy of the order parameter, which gives rise to the observed anisotropy ofM2, can be neglected. We giveP(σ) as a function ofX at low temperature, where the line shape is only weakly dependent onT, and as a function ofT at constantX. It is found that the line shapes andP(σ) in both situations evolve continuously and give no hint of a phase transition. These results are discussed in relation to those of magnetic spin-glasses, and it is concluded that the orientational regime in solid H2, called a quadrupolar glass by previous investigators, cannot be distinguished by symmetry from the orientationally disordered phase that occurs at high temperature.

Third sound and thermal conduction in thin 4 He films

Abstract: The dynamic Kosterlitz-Thouless theory of superfluidity in two dimensions is applied to the problems of third-sound propagation and thermal conduction in thin4He films. Extensions of existing theory are made and the results are compared with experiment.

The Peierls transition and electron localization by a random potential in a one-dimensional conductor

Abstract: The influence of a random impurity potential on a simple model of a one-dimensional metal undergoing a Peierls transition is considered. The following properties are studied: the order parameter, the transition temperature, the state density. Contrary to the “kinetic” approach, where only nonintersecting impurity lines are taken into account, it appears that the energy gap is absent at any impurity concentration, although at small concentrations the state density at the Fermi level decreases exponentially with concentration. The static conductivity of a finite sample is calculated at various temperatures. The formation of a charge density wave enhances localization: the localization length decreases with increasing order parameter. The conductivity at small but finite frequency is obtained. Close to the critical temperature it decreases rapidly withT c -T.

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

Abstract: 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.

Vacancies in a quantum crystal of fermions. The spin polaron in solid 3 He

Abstract: We have studied the properties of a hole tunneling in an alternate lattice of fermions weakly coupled by antiferromagnetic exchange This model is applied to vacancies in solid3He, which has features in common with a Mott semiconductor The vacancy induces a ferromagnetic polarization over a volume limited by exchange and entropy Using a variational method, we describe this structure as a nonlinear excitation This magnetic polaron is stable and self-trapped up to a temperature of the order of the tunneling frequency At higher temperature, the ferromagnetic polarization is destroyed, and the vacancy undergoes a sort of Brownian motion Assuming a vacancy concentration in the range 10−4–10−3, we may account for some low-temperature anomalies observed in the susceptibility, the entropy, and the specific heat of bcc3He Most of these ideas can be applied to excess charge carriers in Mott insulators

Roton liquid theory

Abstract: A mean field approach, analogous to the Landau theory of Fermi liquids, is developed and applied to the interacting roton liquid present in superfluid4He at temperatures below the λ-point. We derive stability conditions for the parameters describing the effective roton-roton interaction and use one of these to place a bound on the variation with temperature of the roton energy. By fitting to experimental results on the specific heat and normal fluid density, we obtain the first two moments of the effective roton interaction.

Atomic disorder and superconductivity in A15 materials

Abstract: The validity of a modified linear chain model for describing the properties of A15 superconductors is discussed in detail. Using this simple model for the electronic density of states, we calculate the critical temperature and the Fermi level as functions of atomic disorder with concentrationc within the framework of the BCS theory. Thereby the experimentally observed saturation effect of the critical temperature is reproduced by taking into account the contribution of three-dimensional electronic states. The microscopic versions of the Ginzburg-Landau equations for systems with a strongly varying electronic density of states and a strongly varying electron velocity are derived for clean and dirty superconductors in order to calculate the Ginzburg-Landau parameter, the coherence length, the penetration depth, and the upper critical field as functions of atomic disorder. It is shown that these quantities depend strongly on the values inserted for the mean free electron pathl(c). Good agreement between theoretical and experimental results is obtained by an appropriate choice ofl(c). In contrast, the thermodynamic critical field is nearly independent ofl(c). In all cases we derive a depression of the pinning forces and the critical current densities with increasing atomic disorder in good agreement with the experiments.

Cutting of bent vortex lines

Abstract: One of the major problems in the application of type II superconductors is the appearance of resistivity in cases where a current-carrying specimen is in a longitudinal magnetic field. This is explained by the onset of flux-line cutting events, followed by cross-joining of the line parts. The calculation given here shows the amount of repulsive force and energy between two curved vortex lines and examines the general stability of the vortex-vortex system. First, the actual interaction potential between curved vortices is computed. It includes all electromagnetic and core overlap terms of interaction and self-interaction, and allows computation of the system energy under all curved vortex-line configurations. A computer program is used to find the form of lowest free energy. To do this, special trial functions are established to describe the three-dimensional form of the vortex-vortex system. In these functions parameters determine the qualitative and quantitative form. The asymptotic boundary conditions are built into the nature of the trial functions. The computer program now minimizes the free energy with respect to these parameters. The resulting repulsive energy and force are more than ten times less than the known results for straight flux lines, especially for small asymptotic cutting angles. There is no sharp maximum in the plot of repulsive force versus flux-line separation. A remarkable result is the loss of general stability below a separation distance of several London penetration depths, depending on the cutting angle and the Ginzburg-Landau parameter. The explanation lies in the local attraction of central sections of the vortices as a result of configurational adaptation. This explains the onset of resistance at small currents and small magnetic fields.

Shear viscosity of the B phase of superfluid 3 He. III

Abstract: We report the calculation of the shear viscosity in superfluid3He-B at 6, 21, and 30 bar. We have used the variational solution of the Boltzmann equation for quasiparticles. The transition probabilities are obtained within thes-p-d-wave approximation by fitting the normal state transport coefficients. The old and new Landau parameters are used to estimate the scattering amplitudes. The reduced shear viscosity does not depend very much on the choice of Landau parameters and agrees very well with experiment in the temperature range 0.5

Transport properties of helium near the liquid-vapor critical point. II. Thermal conductivity of a 3 He- 4 He mixture

Abstract: Measurements of the thermal conductivity are reported for an 80%3He-20%4He mixture above the critical point along several isotherms and near-critical isochores, using the same techniques and apparatus described for a study of3He. Using again the assumption that the observed conductivity λ can be decomposed into a sum of a regular and a singular contribution λreg and λsing, it is shown that along two near-critical isochores, λsing diverges. In particular, along the isochore showing the largest λ at the phase transition, the divergence is nearly the same as for3He and can be roughly characterized by a simple power law (T-Tc)−ψ with Ψ≈0.58. This observation is contrary to predictions that foresee λsing→0 asT c is approached. The relaxation times characterizing the attainment of steady state conditions after switching the heat flux on and off show a similar behaviour as a function of reduced temperature as do those for pure3He. This result might indicate a substantial coupling between concentration and entropy diffusion. In the Appendix, the correlation length for3He nearT c is calculated from heat conductivity, viscosity, and specific heat data.

Low-temperature properties of Ga0.5Mo2S4

Abstract: Specific heat measurements from 2 to 27 K and crystal structure and magnetic properties for 4.2–300 K are reported for the spinel Ga0.5Mo2S4. AtTp=42 K this ternary chalcogenide undergoes a phase transition. At liquid helium temperatures it has a rhombohedral crystal structure with lattice parametera=9.275 A and rhombohedral angle α=90.45°. It follows from the magnetization measurements that ferromagnetic ordering takes place at about 20 K, and close to the Curie point an anomaly in the temperature dependence ofCp has been found. The magnetic behavior of Ga0.5Mo2S4 at low temperatures can be explained by a small concentration of magnetic ions and far-distant-neighbor superexchange interactions partly weakened by vacancies located in 4(c) positions. Magnetocaloric measurements indicate the dominance of ferromagnetic interactions.