Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review Letters

Soundlike Collective Excitations in Superfluid He3

P. Wölfle

Published Dec 10, 1973• 32 citations
Publisher

Abstract

I discuss soundlike collective excitations in anisotropic superfluid Fermi liquids in both the collisionless and the hydrodynamic regimes. Expressions for the velocities of zero, first, second, and fourth sound are derived in terms of the Landau parameters of the normal state. The second- and fourth-sound velocities are found to vary appreciably with orientation.

DOI
10.1103/physrevlett.31.1437

Related papers

Propagation of second sound in a superfluid Fermi gas in the unitary limit

Emiko Arahata, Tetsuro Nikuni

We study sound propagation in a uniform superfluid gas of Fermi atoms in the unitary limit. The existence of normal and superfluid components leads to appearance of two sound modes in the collisional regime, referred to as first and second sounds. The second sound is of particular interest as it is a clear signal of a superfluid component. Using Landau's two-fluid hydrodynamic theory, we calculate hydrodynamic sound velocities and these weights in the density response function. The latter is used to calculate the response to a sudden modification of the external potential generating pulse propagation. The amplitude of a pulse which is proportional to the weight in the response function is calculated, the basis of the approach of Nozi\`eres and Schmitt-Rink for the BCS-BEC. We show that, in a superfluid Fermi gas at unitarity, the second-sound pulse is excited with an appreciate amplitude by density perturbations.

arXiv:0907.2743•Physical Review A•Oct 19, 2009•28 citations

Anisotropic-Fermi-liquid theory of ultracold fermionic polar molecules: Landau parameters and collective modes

Ching-Kit Chan, Congjun Wu, Wei-Cheng Lee +1 more

We study the Fermi liquid properties of the cold atomic dipolar Fermi gases with the explicit dipolar anisotropy using perturbative approaches. Due to the explicit dipolar anisotropy, Fermi surfaces exhibit distortions of the ${d}_{{r}^{2}\ensuremath{-}3{z}^{2}}$ type in three dimensions and of the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ type in two dimensions. The fermion self-energy, effective mass, and Fermi velocity develop the same anisotropy at the Hartree-Fock level proportional to the interaction strength. The Landau interaction parameters in the isotropic Fermi liquids become the tridiagonal Landau interaction matrices in the dipolar Fermi liquids which renormalize thermodynamic susceptibilities. With large dipolar interaction strength, the Fermi surface collapses along directions perpendicular to the dipole orientation. The dynamic collective zero sound modes exhibit an anisotropic dispersion with the largest sound velocity propagating along the polar directions. Similarly, the longitudinal $p$-wave channel spin mode becomes a propagating mode with an anisotropic dispersion in multicomponent dipolar systems.

arXiv:0906.4403•Physical Review A•Feb 5, 2010•73 citations

First, Second, and Quasi-Particle Sound

Philippe Nozières, David Pines

The wave propagation might be appropriately called quasi-particle sound, since in the long wave-length limit the only density fluctuations of importance are those produced by exciting a single quasi-particle from the condensate. Quasi-particle sound has essentially the same physical origin as zero sound in a Fermi liquid. The quasi-particle sound velocity will be temperature dependent, since the energy of a given quasi-particle depends on the thermal excitation of other quasi-particles. Superfluid hydrodynamics is richer than its Fermi liquid counterpart because one can have relative motion of the thermal quasi-particles and the condensate. This chapter describes the propagation of first and second sound in the hydrodynamic limit and then go on to a consideration of quasi-particle sound in the collisionless regime. A wide variety of irreversible phenomena which have as their physical origin collisions between the thermally-excited quasi-particles.

CRC Press eBooks•Mar 5, 2018•0 citations

Three Sound Modes in a Bose–Fermi Superfluid Mixture at Finite Temperatures

Yosuke Ono, Rei Hatsuda, Kenta Shiina +2 more

We study sound propagation in a Bose–Fermi superfluid mixture at finite temperatures. Sound modes in the mixture are described by the extended Landau's hydrodynamic theory. Our extended Landau's hydrodynamic theory shows that three sound modes exist. We calculate the hydrodynamic sound velocities and weights in the density response function based on the approach of Noziéres and Schmitt-Rink for the BCS to Bose–Einstein condensation crossover. In a Bose–Fermi superfluid mixture, the three sound mode pulses can be excited with an appreciable amplitude by density perturbations.

Journal of the Physical Society of Japan•Feb 18, 2019•1 citation

Soft modes in Fermi liquids at arbitrary temperatures

D. Belitz, T. R. Kirkpatrick

We use kinetic-theory methods to analyze Landau Fermi-liquid theory, and in particular to investigate the number and nature of modes in Fermi liquids that are soft in the long-wavelength limit, both in the hydrodynamic and the collisionless regimes. In the hydrodynamic regime we show that Fermi-liquid theory is consistent with Navier-Stokes hydrodynamics at all temperatures, as expected. The soft modes are the ones familiar from classical hydrodynamics that are controlled by the five conservation laws; namely, two first-sound modes, two shear diffusion modes, and one heat diffusion mode. These modes have a particle-like spectrum and are soft, or scale invariant, at all temperatures. In the collisionless regime we show that the entire single-particle distribution function is soft with a continuous part of the spectrum. This continuous soft mode, which is well known but often not emphasized, has important physical consequences, e.g., for certain quantum phase transitions. In addition, there are the well-known soft zero-sound excitations that describe angular fluctuations of the Fermi surface; their spectra are particle-like. They are unrelated to conservation laws, acquire a mass at any nonzero temperature, and their number depends on the strength of the quasiparticle interaction. We also discuss the fates of these two families of soft modes as the temperature changes. With increasing temperature the size of the collisionless regime shrinks, the damping of the modes grows, and eventually all of the collisionless modes become overdamped. In their stead the five hydrodynamic modes appear in the hydrodynamic regime at asymptotically low frequencies. The two families of soft modes are unrelated and have very different physical origins. In charged Fermi liquids the first-sound modes in the hydrodynamic regime and the $\ensuremath{\ell}=0$ zero-sound modes in the collisionless regime get replaced by plasmons, all other modes remain soft.

arXiv:2112.14246•Physical review. B./Physical review. B•Jun 29, 2022•7 citations

Dynamical Effects of the Landau ParameterF2in Normal Fermi Liquids

S. Tasaki, Fukuo Yoshida

Collective density excitations are studied in Ferrni liquids, with particular attention to the role of the Landau parameter of the second order F 2 . The density response function χ( k , z ) including F 2 is obtained by solving the Landau transport equation in the collisionless regime. From comparison of it with an formal expression in the small wavenumber limit, a relation is pointed out between F 2 and a pair correlation function. It is also found that there exists a critical value of F 2 above which χ( k , z ) exhibits two poles outside the continuum region. Zero-sound modes and their intensities, as well as the dynamical structure factor S ( k ,ω), are evaluated below and above the critical value. Discussion is also given on the F 2 -dependence of S ( k ,ω) at non-zero wavenumbers.

Journal of the Physical Society of Japan•May 15, 1989•1 citation
I discuss soundlike collective excitations in anisotropic superfluid Fermi liquids in both the collisionless and the hydrodynamic regimes. Expressions for the velocities of zero, first, second, and fourth sound are derived in terms of the Landau parameters of the normal state. The second- and fourth-sound velocities are found to vary appreciably with orientation.
We study sound propagation in a uniform superfluid gas of Fermi atoms in the unitary limit. The existence of normal and superfluid components leads to appearance of two sound modes in the collisional regime, referred to as first and second sounds. The second sound is of particular interest as it is a clear signal of a superfluid component. Using Landau's two-fluid hydrodynamic theory, we calculate hydrodynamic sound velocities and these weights in the density response function. The latter is used to calculate the response to a sudden modification of the external potential generating pulse propagation. The amplitude of a pulse which is proportional to the weight in the response function is calculated, the basis of the approach of Nozi\`eres and Schmitt-Rink for the BCS-BEC. We show that, in a superfluid Fermi gas at unitarity, the second-sound pulse is excited with an appreciate amplitude by density perturbations.
We study the Fermi liquid properties of the cold atomic dipolar Fermi gases with the explicit dipolar anisotropy using perturbative approaches. Due to the explicit dipolar anisotropy, Fermi surfaces exhibit distortions of the ${d}_{{r}^{2}\ensuremath{-}3{z}^{2}}$ type in three dimensions and of the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ type in two dimensions. The fermion self-energy, effective mass, and Fermi velocity develop the same anisotropy at the Hartree-Fock level proportional to the interaction strength. The Landau interaction parameters in the isotropic Fermi liquids become the tridiagonal Landau interaction matrices in the dipolar Fermi liquids which renormalize thermodynamic susceptibilities. With large dipolar interaction strength, the Fermi surface collapses along directions perpendicular to the dipole orientation. The dynamic collective zero sound modes exhibit an anisotropic dispersion with the largest sound velocity propagating along the polar directions. Similarly, the longitudinal ppp-wave channel spin mode becomes a propagating mode with an anisotropic dispersion in multicomponent dipolar systems.
The wave propagation might be appropriately called quasi-particle sound, since in the long wave-length limit the only density fluctuations of importance are those produced by exciting a single quasi-particle from the condensate. Quasi-particle sound has essentially the same physical origin as zero sound in a Fermi liquid. The quasi-particle sound velocity will be temperature dependent, since the energy of a given quasi-particle depends on the thermal excitation of other quasi-particles. Superfluid hydrodynamics is richer than its Fermi liquid counterpart because one can have relative motion of the thermal quasi-particles and the condensate. This chapter describes the propagation of first and second sound in the hydrodynamic limit and then go on to a consideration of quasi-particle sound in the collisionless regime. A wide variety of irreversible phenomena which have as their physical origin collisions between the thermally-excited quasi-particles.
We study sound propagation in a Bose–Fermi superfluid mixture at finite temperatures. Sound modes in the mixture are described by the extended Landau's hydrodynamic theory. Our extended Landau's hydrodynamic theory shows that three sound modes exist. We calculate the hydrodynamic sound velocities and weights in the density response function based on the approach of Noziéres and Schmitt-Rink for the BCS to Bose–Einstein condensation crossover. In a Bose–Fermi superfluid mixture, the three sound mode pulses can be excited with an appreciable amplitude by density perturbations.
We use kinetic-theory methods to analyze Landau Fermi-liquid theory, and in particular to investigate the number and nature of modes in Fermi liquids that are soft in the long-wavelength limit, both in the hydrodynamic and the collisionless regimes. In the hydrodynamic regime we show that Fermi-liquid theory is consistent with Navier-Stokes hydrodynamics at all temperatures, as expected. The soft modes are the ones familiar from classical hydrodynamics that are controlled by the five conservation laws; namely, two first-sound modes, two shear diffusion modes, and one heat diffusion mode. These modes have a particle-like spectrum and are soft, or scale invariant, at all temperatures. In the collisionless regime we show that the entire single-particle distribution function is soft with a continuous part of the spectrum. This continuous soft mode, which is well known but often not emphasized, has important physical consequences, e.g., for certain quantum phase transitions. In addition, there are the well-known soft zero-sound excitations that describe angular fluctuations of the Fermi surface; their spectra are particle-like. They are unrelated to conservation laws, acquire a mass at any nonzero temperature, and their number depends on the strength of the quasiparticle interaction. We also discuss the fates of these two families of soft modes as the temperature changes. With increasing temperature the size of the collisionless regime shrinks, the damping of the modes grows, and eventually all of the collisionless modes become overdamped. In their stead the five hydrodynamic modes appear in the hydrodynamic regime at asymptotically low frequencies. The two families of soft modes are unrelated and have very different physical origins. In charged Fermi liquids the first-sound modes in the hydrodynamic regime and the $\ensuremath{\ell}=0$ zero-sound modes in the collisionless regime get replaced by plasmons, all other modes remain soft.
Collective density excitations are studied in Ferrni liquids, with particular attention to the role of the Landau parameter of the second order F 2 . The density response function χ( k , z ) including F 2 is obtained by solving the Landau transport equation in the collisionless regime. From comparison of it with an formal expression in the small wavenumber limit, a relation is pointed out between F 2 and a pair correlation function. It is also found that there exists a critical value of F 2 above which χ( k , z ) exhibits two poles outside the continuum region. Zero-sound modes and their intensities, as well as the dynamical structure factor S ( k ,ω), are evaluated below and above the critical value. Discussion is also given on the F 2 -dependence of S ( k ,ω) at non-zero wavenumbers.