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arXiv:2602.04612 · Annalen der Physik

Density Modulations of Zero Sound

L. Pisani

Published Feb 1, 2026• 0 citations
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Abstract

ABSTRACT We study the density modulation of an interacting Fermi gas caused by the uniform motion of an impurity at zero temperature. For strong enough interaction among atoms, the modulation propagates thanks to the excitation of the collective zero sound mode if the impurity speed is above the zero sound threshold. We are able to assess, via a semi‐analytic evaluation, the extent of the zero sound contribution to the density oscillation over and above the incoherent background of particle‐hole excitations. Given the strong dependence of the results on the features of the gas interaction potential, we also analyze how they vary depending on its strength, range and shape.

DOI
10.1002/andp.202500478

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ABSTRACT We study the density modulation of an interacting Fermi gas caused by the uniform motion of an impurity at zero temperature. For strong enough interaction among atoms, the modulation propagates thanks to the excitation of the collective zero sound mode if the impurity speed is above the zero sound threshold. We are able to assess, via a semi‐analytic evaluation, the extent of the zero sound contribution to the density oscillation over and above the incoherent background of particle‐hole excitations. Given the strong dependence of the results on the features of the gas interaction potential, we also analyze how they vary depending on its strength, range and shape.
We investigate collective excitations in a dipolar and non-dipolar Fermi gas mixture at zero temperature.We obtain the density-density correlation functions of the mixtures in the ring diagram approximation.We analyze the dispersion relation determined by the poles of the density-density correlation functions and find two different types of collective modes: the undamped zero sound and the overdamped modes.We show that the undamped zero sound mode exists only at long wavelengths and the speed of undamped zero sound varies with the propagation direction due to an anisotropy of the dipolar interaction between dipolar fermions.We also show that the decay rate of the overdamped mode decreases as the inter-particle interaction strength between dipolar and non-dipolar fermions increases and the overdamped mode is replaced by unstable one if the inter-particle interaction strength is much strong.
Landau showed that a nonideal Fermi gas at zero temperature can sustain collective oscillations of the acoustical type (zeroth sound). The altenuation of zeroth sound in a dilute Fermi gas with repulive intereacitions was considered. The problem was formulted interms of the Green function G which describes the paropation of density fluctuations through the system. The simplest approximation of G led to Landau's dispersion law which wae analyzed in some detail. The contribution of the phonons' zero point oscillations to the ground- state energy was estimated and found to lead to a term which has an essential singuarty at the origin of the coupling constant plane. The energy and width of the phonon are given by the poles in the spectral representation of G, and the location of these poles was determined from the Fredholm solution of an apparoximate integral equation satisfied by G. In this way it is showa that ths width, divided by the displacement of the collective state above the single- particle continunna of the free gas, vanishes linearly in the long wavelength limit. It is also shows that in the limit of extreme dilution the correct damping; can be obtained by merely taking the finite lifetimemore » of single-particles excitations into account and ignoring the dissipative effects of the noninstantaneous interactions betweein the particles in the medium. Finally, it is alao argued that the Fredholm method is the natural tool for discussing many problems in the theory of collective motion. (auth)« less
We study zero sound in a weakly interacting two-dimensional (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.
Abstract We consider a weakly-interacting fermionic gas of alkali-metal atoms characterized by two hyperfine states which are Rabi coupled. By using a Born approximation for the repulsive interaction we determine the zero-temperature equation of state of this Fermi gas in D spatial dimensions ( D = 1, 2, 3). Then, adopting the Landau–Vlasov equation and hydrodynamic equtions, we investigate the speed of first sound and zero sound. We show that the two sounds, which occur respectively in collisional and collisionless regimes, crucially depend on the interplay between interaction strength and Rabi coupling. Finally, we discuss for some experimentally relevant cases the effect of a trapping harmonic potential on the density profles of the fermionic system.
Collective density excitation spectrum in two-component Fermi gases is dominated by conventional optical plasmon at high frequencies and charge neutral gapless acoustic mode in the quasi-classical domain. In this work we reveal the identity between the latter acoustic plasmon and zero sound propagating in the slow component. Within the framework of two coupled collisionless kinetic equations with self-consistent electrostatic potential, we show that the mode stability to the long-range intracomponent Coulomb interaction is determined by the static screening by the fast quasiparticles. Depending on the magnitude of the effective Landau interaction parameter given by the ratio of Thomas-Fermi wavevectors in components, acoustic plasmon undergoes transformation from zero sound in almost ideal Fermi gas to ion-acoustic wave in both two and three dimensions. As it was recently shown for the particular case of type-I Weyl semimetals [Afanasiev, Greshnov and Svintsov, Phys. Rev. B 103, 205201 (2021)], strongly anisotropic two-component solid state plasma is a natural platform hosting this acoustic plasmon-zero sound mode which is experimentally accessible via standard energy-loss and time-domain techniques.
We study the zero sound and the first sound in a dilute and ultracold disk-shaped normal Fermi gas with a strong harmonic confinement along the axial direction and uniform in the two planar directions. Working at zero temperature we calculate the chemical potential $\ensuremath{\mu}$ of the fermionic fluid as a function of the uniform planar density $\ensuremath{\rho}$ and find that $\ensuremath{\mu}$ changes its slope in correspondence to the filling of harmonic axial modes (shell effects). Within the linear response theory, and under the random phase approximation, we calculate the velocity cs0{c}_{s}^{0}cs0​ of the zero sound. We find that also cs0{c}_{s}^{0}cs0​ changes its slope in correspondence of the filling of the harmonic axial modes and that this effect depends on the Fermi-Fermi scattering length aF{a}_{F}aF​. In the collisional regime, we calculate the velocity cs{c}_{s}cs​ of first sound showing that cs{c}_{s}cs​ displays jumps at critical densities fixed by the scattering length aF{a}_{F}aF​. Finally, we discuss the experimental achievability of these zero sound and first sound waves with ultracold alkali-metal atoms.