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Register a new userCompeting solutions of Landaus kinetic equation for zero sound and first sound in thin arbitrarily polarized Fermi-liquid films
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We examine in detail the method introduced by Sanchez-Castro, Bedell, and Wiegers (SBW) to solve Landaus linearized kinetic equation, and compare it with the well-known standard method introduced by Abrikosov and Khalatnikov (AK). The SBW approach, hardly known, differs from AK in the way that moments are taken with respect to the angular functions of the Fourier transformed kinetic equation. We compare the SBW and AK solutions for zero-sound and first-sound propagation speeds and attenuation both analytically in the zero and full polarization limits, and numerically at arbitrary polarization using Landau parameters appropriate for thin $^{3}$He films. We find that the lesser known method not only yields results in close agreement with the standard method, but in most cases does so with far less analytic and computational
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We calculate expressions for the state-dependent quasiparticle lifetime, the thermal conductivity $kappa$, the shear viscosity $eta$, and discuss the spin diffusion coefficient $D$ for Fermi-liquid films in two dimensions. The expressions are valid for low temperatures and arbitrary polarization. The low-temperature expressions for the transport coefficients are essentially exact. We find that $kappa^{-1} sim T ln{T}$, and $eta^{-1} sim T^{2}$ for arbitrary polarizations $0 le {mathcal{P}} le 1$. We note that the shear viscosity requires a unique analysis. We utilize previously determined values for the density and polarization dependent Landau parameters to calculate the transition probabilities in the lowest order $ell = 0$ approximation, and thus we obtain predictions for the density, temperature and polarization dependence of the thermal conductivity, shear viscosity, and spin diffusion coefficient for thin he3 films. Results are shown for second layer he3 films on graphite, and thin he3-he4 superfluid mixtures. The density dependence is discussed in detail. For $kappa$ and $eta$ we find roughly an order of magnitude increase in magnitude from zero to full polarization. For $D$ a simialr large increase is predicted from zero polarization to the polarization where $D$ is a maximum ($sim 0.74$). We discuss the applicability of he3 thin films to the question of the existence of a universal lower bound for the ratio of the shear viscosity to the entropy density.
We derive the quantum Boltzmann equation (QBE) by using generalized Landau-interaction parameters, obtained through the nonequilibrium Greens function technique. This is a generalization of the usual QBE formalism to non-Fermi liquid (NFL) systems, which do not have well-defined quasiparticles. We apply this framework to a controlled low-energy effective field theory for the Ising-nematic quantum critical point, in order to find the collective excitations of the critical Fermi surface in the collisionless regime. We also compute the nature of the dispersion after the addition of weak Coulomb interactions. The zero angular momentum longitudinal vibrations of the Fermi surface show a linear-in-wavenumber dispersion, which corresponds to the zero sound of Landaus Fermi liquid theory. The Coulomb interaction modifies it to a plasmon mode in the long-wavelength limit, which disperses as the square-root of the wavenumber. Remarkably, our results show that the zero sound and plasmon modes show the same behaviour as in a Fermi liquid, although an NFL is fundamentally different from the former.
Bulk superfluid helium supports two sound modes: first sound is an ordinary pressure wave, while second sound is a temperature wave, unique to inviscid superfluid systems. These sound modes do not usually exist independently, but rather variations in pressure are accompanied by variations in temperature, and vice versa. We studied the coupling between first and second sound in dilute $^3$He - superfluid $^4$He mixtures, between 1.6 K and 2.2 K, at $^3$He concentrations ranging from 0 to 11 %, under saturated vapor pressure, using a quartz tuning fork oscillator. Second sound coupled to first sound can create anomalies in the resonance response of the fork, which disappear only at very specific temperatures and concentrations, where two terms governing the coupling cancel each other, and second sound and first sound become decoupled.
We study zero sound in a weakly interacting 2D gas of single-component fermionic dipoles (polar molecules or atoms with a large magnetic moment) tilted with respect to the plane of their translational motion. It is shown that the propagation of zero sound is provided by both mean field and many-body (beyond mean field) effects, and the anisotropy of the sound velocity is the same as the one of the Fermi velocity. The damping of zero sound modes can be much slower than that of quasiparticle excitations of the same energy. One thus has wide possibilities for the observation of zero sound modes in experiments with 2D fermionic dipoles, although the zero sound peak in the structure function is very close to the particle-hole continuum.
This paper is devoted to the investigation of electron sound -- oscillations of the electron distribution function coupled with elastic deformation and propagating with the Fermi velocity. The amplitude-phase relations characterizing the behavior of the electron sound in Ga single crystals are determined experimentally. A model problem of excitation of electron sound in a compensated metal with equivalent bands is solved for a finite sample with diffusive scattering of electrons at the interfaces. It was found that the displacement amplitude of the receiving interface is two orders of magnitude larger than the elastic amplitude of the wave due to electron pressure. It was established that the changes occurring in the amplitude and phase of the electron sound waves at a superconducting transition do not depend on the path traversed by the wave, i.e. they refer only to the behavior of the transformation coefficient.
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