The transition from first sound to zero sound in a normal Fermi liquid

The properties of sound in a Fermi liquid are discussed for the case when the frequency of the wave is comparable with the collision frequency. We show that if the zero-sound velocity is very much greater than the Fermi velocity, as it is in liquid ³ He, the kinetic equation is of the same form as for the frequency-dependent conductivity of a normal Fermi liquid. By employing upper and lower bounds for the frequency-dependent conductivity obtained by Ah-Sam, Højgaard Jensen, and Smith, we obtain bounds on the velocity and attenuation of sound. Other bounds, which are in many cases better than these, have also been found and employed. Both the velocity and attenuation are reduced compared with what one would expect on the basis of a simple interpolation formula consistent with the exact results for the zero-sound and first-sound regimes. For liquid ³ He the reductions in the attenuation are expected to be of the order of about3%.Research supported in part by NSF grant DMR 76-24011.     

Anisotropic attenuation of zero sound in superfluid3He-A

The anisotropic attenuation of zero sound in superfluid³He-A at 29.3 bar pressure has been measured at 24.4, 34.2, 44.2, 54.0, 63.9, 73.7, 83.5, and 93.4 MHz. The clapping mode resonance has been observed at all frequencies, and the reentrant normal flapping resonance has been measured for the first time. Analysis of these results leads to anf-wave pairing parameter,x ₃ ^–1 –0.1±0.05, and a determination of strong coupling corrections to the energy gap far fromT _c. This is expressed by an enhancement of the zero-temperature energy gap by a factor 1.3±0.1 above that of weak coupling, 2.03k _B T _c . The clapping mode data is consistent with a nontrivial, strong coupling correction to the mode frequency, reducing it by 6%. The³He was confined to a slab 250 µm in thickness and the superfluid texture was oriented by a magnetic field. This allowed attenuations up to 100 cm^–1 to be resolved and the attenuation from pair-breaking processes alone to be determined for the first time. The sound attenuation was measured for angles between the sound propagation direction and the1vector of 0, /4, and /2. The sensitivity of the numerically evaluated attenuation to quasiparticle collision time,f-wave parameter, and uniformity of the orbital texture is explored.     

On the dispersion of zero sound in liquid4He

A new derivation of Pines' zero-sound model of the phonon in liquid⁴He is presented which shows that the essential assumption in the model is that the mechanism of phonon damping in no way depends upon the mechanism for creating phonon modes. The result of a numerical calculation of the dispersion relation for zero sound in the wave number range 0≤k≤0.2 Å^?1 is given and is shown to be in very good agreement with recent direct measurements of the speed of superthermal phonons in He II by Narayanamurti, Andres, and Dynes.     

Investigation of low-temperature electron relaxation by zero sound attenuation

We develop a new method of investigation of low-temperature electron relaxation \in metals, based on the analysis of the temperature dependences of the attenuation of zero sound excited by ultrasonic pulses. We have discovered that these dependences obtained in the temperature region about of 1–8 K reproduce directly the temperature behavior of the electron scattering rate. The main features of our method are its insensitivity to small-angle scattering and the additivity of contributions of various relaxation processes to the total scattering rate. Both the theoretical analysis of zero-sound propagation in various damping regimes and special experiments produced for gallium confirm the validity of our consideration. We have identified the considerable contribution of electron-electron collisions in all investigated metals (gallium, aluminum, molybdenum, and tungsten) in the whole studied temperature interval and established the dominating role of Umklapp processes in the zero-sound damping at T >- 4 K for gallium and most probably for tungsten. We interpret the latter result as the first experimental observation of Peierls' exponent in polyvalent metals in zero magnetic field. The values obtained for electron-electron and electron-phonon scattering rates are compared with known experimental data and theoretical estimations.     

On the attenuation and dispersion of first sound near the superfluid transition in He4

In this paper available measurements of the attenuation and dispersion of first sound near the superfluid transition in He⁴ are re-examined. Particular attention is given to the effect of the gravitational inhomogeneity upon the measurements, and the thermodynamic velocity is used to obtain the dispersion contribution from measured velocities at nonzero frequencies. The re-interpreted results are discussed in terms of current theories. Although there is partial agreement between experiment and theory, a number of aspects of the problem requires further theoretical and experimental investigation.     

The effects of frequency-dependent attenuation and dispersion on sound speed measurements: applications in human trabecular bone

Sound speed may be measured by comparing the transit time of a broadband ultrasonic pulse transmitted through an object with that transmitted through a reference water path. If the speed of sound in water and the thickness of the sample are known, the speed of sound in the object may be computed. To measure the transit time differential, a marker such as a zero-crossing, may be used. A sound speed difference between the object and water shifts all markers backward or forward. Frequency-dependent attenuation and dispersion may alter the spectral characteristics of the waveform, thereby distorting the locations of markers and introducing variations in sound-speed estimates. Theory is derived to correct for this distortion for Gaussian pulses propagating through linearly attenuating, weakly dispersive media. The theory is validated using numerical analysis, measurements on a tissue mimicking phantom, and on 24 human calcaneus samples in vitro. Variations in soft tissue-like media are generally not exceptionally large for most applications but can be substantial, particularly for high bandwidth pulses propagating through media with high attenuation coefficients. At 500 kHz, variations in velocity estimates in bone can be very substantial, on the order of 40 to 50 m/s because of the high attenuation coefficient of bone. In trabecular bone, the effects of frequency-dependent attenuation are considerable, and the effects of dispersion are negligible.     

Damping of fourth sound in4He due to normal fluid flow

Measurements of the attenuation of fourth sound were made in superfluid⁴He contained in several porous media with characteristic sizes sufficiently large to permit some normal fluid flow. The data are for pressures between vapor pressure and 25 bar and for temperatures between 1.4 K and the-line. The attenuation was dominated by viscous dissipation associated with the normal fluid flow. For a given medium, it varied by nearly two orders of magnitude over the pressure and temperature range of the experiment. Analysis of the data along isobars and isotherms in terms of an idealized model for the porous medium yielded a unique temperature- and pressure-independent characteristic size for each medium.     

Propagation of zero sound in the Balian-Werthamer state

The propagation of zero sound in the superfluid state of the type suggested by Balian and Werthamer is studied theoretically. In the collisionless limit the attenuation of zero sound takes place only for ω≥2Δ(T) and at ω=2(3/5)^1/2Δ(T), where ω is the frequency of the sound wave and Δ(T) is the temperature-dependent order parameter.     

Wave dispersion and attenuation in fiber composites

 This work deals with the dispersion and attenuation of elastic plane waves propagating in a single layer fiber reinforced composite, in a direction which is perpendicular to the fibers. An iterative effective medium model, based on single scattering considerations, for the quantitative estimation of wave dispersion and attenuation is proposed. The single scattering problem is solved numerically by means of a 2-D boundary element methodology. Numerical results concerning the plane velocity and the attenuation coefficient of longitudinal or transverse SH, SV waves propagating in two types of fiber reinforced composite materials, are presented. The obtained results are compared to those taken either experimentaly or numericaly by other investigators.     

Ultrasonic attenuation and sound velocity of the excitonic state

Ultrasonic attenuation and sound velocity of a metal in the excitonic state are investigated theoretically in the limitq1 1 and/T _c 1, whereq is the sound-wave vector,1 is the electron mean-free path, is the phonon energy, andT _c is the transition temperature of the excitonic state. The attenuation coefficient of the longitudinal wave increases drastically upon entrance into the excitonic state, then passes a maximum and decreases exponentially as temperature tends to 0 K. The attenuation coefficient of the transverse wave, on the other hand, is described in terms of the electric conductivity in the limitq1 1 and generally increases in the excitonic state. Furthermore, we find that the sound velocity of the longitudinal wave increases rapidly in the excitonic state, which is a simple manifestation of the anomaly of the dielectric function in the excitonic state.     

Impurity distributions in crystals due to growth-rate fluctuations

Balance equations for the second moments of the velocity and temperature fluctuations are used to examine the effects of turbulent natural convection on the uniformity of impurity distributions in crystals.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 50, No. 5, pp. 806–810, May, 1986.     

Attenuation of zero sound in oriented liquid3He-A

Systematic measurements of the change – _c of the absorption coefficient for zero sound in³He-A from its value atT _c are presented for both 24.08 and 33.53 bar and several frequencies. The³He-A is oriented by means of a magnetic field, so only the case where field and sound directions are parallel give results which can be reliably compared with theory. We find that for 5-MHz zero sound at temperatures well below the collective modes peak there is a substantial anisotropy of the attenuation. We also find at high enough frequency a linear relationship between the sonic frequency and the location on a(1–T/T _c)^1/2 scale of the collective modes peak forl·q=0. Comparison of theory and experiment for these data is excellent and suggests that the method may be an accurate one for measuring the temperature dependence of the energy gap in³He-A.Work supported by the U.S. Energy Research and Development Administration under contract number E(04-3)-34 P.A. 143.     

Measurement of the velocity and attenuation of fourth sound in helium II

The velocity and the attenuation of fourth sound have been measured in liquid helium at temperatures between 0.8 K and the point, along the vapor pressure curve. The measurements were made using the resonance technique and the helium was contained between small pores in packed powder specimens. From the velocity, it could be determined that the sound propagates under adiabatic conditions. According to theory, the attenuation of fourth sound consists of two contributions: surface losses due to heat exchange with the resonator body and volume losses due to dissipative processes associated with the viscosity coefficients and ₃. The results of our attenuation measurements are in agreement with this theory; however, it appears that the attenuation is affected at low temperatures, if the mean free path of an elementary excitation becomes comparable to or larger than the mean pore diameter of the packed powder samples.This work was supported in part by the Deutsche Forschungsgemeinschaft. It is part of the dissertation (D77) of H.-J. Lauter.     

Transverse zero sound and the LandauF 2 parameter in liquid3He

The Boltzmann equation for the quasiparticle distribution in theT 0 limit of a Landau Fermi liquid is solved by Fourier-Laplace transformation, following a method described in a previous paper. An initial sinusoidal transverse velocity distribution is assumed, leading in the hydrodynamic limit to an overdamped solution and in the zero-sound limit to damped transverse standing waves. The velocityc _t of transverse zero sound obeysc _t ² = _s /, where _s is the shear modulus. One can estimatec _t and _s from the Fermi velocity, sincec _t V _F. Using the solutions to calculate the pressure and velocity gradient, one can estimate the shear viscosity by taking the ratio of these quantities, giving = _{s s} , where _s is a relaxation time of the order of the relaxation time for shear stress. Similarly, calculation of the heat flux and temperature gradient gives the thermal conductivity in terms of the Landau parametersF ₁ andF ₂ .A fit of the theoretical expression to experimental values of suggests thatF ₂ <0, which is also a necessary condition for convergence of the solution obtained.     

The spin diffusion in normal and superfluid Fermi liquids

Spin diffusion in paramagnetic spin systems is a dissipative process which acts so as to remove all spatial variation of the magnetization. In normal and superfluid Fermi liquids its physical origin lies in the nonconservation property of the macroscopic magnetization current associated with the thermal excitations, the Landau and Bogoliubov quasiparticles, respectively. In the hydrodynamic limit this dissipative process manifests itself in a constitutive relation connecting the decaying magnetization current with gradients in the magnetization density via a coefficient of spin diffusion. Exchange contributions to the quasiparticle interaction introduce, in addition, reactive processes, which can be associated with a rotation of the quasiparticle spin current about the direction of the spin polarization. This so-called spin current rotation—or Leggett-Rice effect—leads to nonhydrodynamic behavior of the spin diffusion whenever the exchange frequency becomes comparable to the inverse spin current relaxation time. In this article I would like to review our current understanding of diffusional spin transport, as influenced by nonhydrodynamic effects, in normal and superfluid Fermi systems.Dedicated to Ludwig Tewordt on the occasion of his 65th birthday.     

Metastability-induced charge and spin fluctuations in 123 type superconductors

Various defects arising from lattice mismatch and coordination incompatibility at the cation sites are known to lend the cuprates a metastable state at temperatures and pressures where they exhibit superconductivity. The present paper considers the metastability induced by coordination incompatibility at Cu(1) sites in oxygen-deficient 123 type systems and looks for their possible effects on charge and spin degrees of freedom. Depending upon the concentration of oxygen vacancies, the resulting unstable charge state at the Cu(1) sites is shown to either temporally fluctuate or spatially equilibrate, providing a mechanism for the 90 K and the 60 K plateaus, with a peak in the former observed in the YBa₂Cu₃O_7-y , samples prepared under thermodynamic equilibrium conditions.     

Contribution of the acoustic-wake effect to the attenuation of sound in dilute suspensions of rigid particles

This work deals with the attenuation of sound in dilute suspensions of rigid particles when the hydrodynamic mechanism of the acoustic-wake effect is considered. The study extends a previous model by considering asymmetric flow-field conditions around the particles, caused by other neighbor particles along the direction of propagation of the acoustic field. The attenuation coefficient is derived from the force equation for a spherical particle in an incompressible fluid that is oscillating at low frequencies and amplitudes within the range of Reynolds numbers of 0.1相似文献   

The influence off-wave pairing fluctuations on sound propagation in superfluid3He-A

The theory of sound propagation in pair-correlated Fermi liquids developed previously by Wölfle, with additionalf-wave pairing fluctuations, is applied to the ABM state. Expressions for the anisotropic sound absorption and velocity at arbitrary temperature and frequency in the collisionless limit are derived. Thef-wave pairing fluctuations give a large effect on the normal-flapping mode frequency at low temperatures. The corresponding shift in the sound attenuation peak of this collective mode provides a sensitive probe of thef-wave pair coupling constantg ₃. There is also a pronounced effect on the super-flapping mode attenuation peak, which becomes well defined whenf-wave pairing fluctuations are considered.     

Ultrasonic attenuation in normal and superconducting indium

Measurements have been made of the ultrasonic attenuation in the normal and superconducting states of pure In single crystals. The measurements spanned the frequency range of 6–66 MHz. The data, taken in the amplitude-independent regime, displayed the expected deviations from the BCS-type attenuation which are generally attributed to dislocation attenuation as described by Granato and Lücke. Earlier attempts to use this theory to study the amplitude-independent dislocation attenuation of ultrasound in superconductors (e.g., Mason) were generally limited to very narrow frequency ranges. These earlier results were in general agreement with the Granato and Lücke theory. However, the present multiple-frequency measurements are shown to be inconsistent with the Granato and Lücke theory.Supported by the Applied Research Laboratory of The Pennsylvania State University, under contract with the U.S. Naval Sea Systems Command.