Collective vibrations in a finite Fermi system are studied within a phase space approach which is based on the Landau-Vlasov kinetic equation. The linear response theory is used and the semiclassical internal and collective response functions are evaluated with a continuous single-particle angular momentum $l.$ We focus on the strength function and fragmentation width of the vibrations. We determine the contributions to the collective strength function which are associated with different values of relevant single-particle angular momentum. Applications to the nuclear isoscalar vibrations with multipolarities $L=0,$ 2, and 3 are presented.Collective vibrations in a finite Fermi system are studied within a phase space approach which is based on the Landau-Vlasov kinetic equation. The linear response theory is used and the semiclassical internal and collective response functions are evaluated with a continuous single-particle angular momentum $l.$ We focus on the strength function and fragmentation width of the vibrations. We determine the contributions to the collective strength function which are associated with different values of relevant single-particle angular momentum. Applications to the nuclear isoscalar vibrations with multipolarities $L=0,$ 2, and 3 are presented.

Physical Review CMay 1, 19987 citations

Atypical behavior of collective modes in two-dimensional Fermi liquids

M P Gochan, J T Heath, K S Bedell

Abstract Using the Landau kinetic equation to study the non-equilibrium behavior of interacting Fermi systems is one of the crowning achievements of Landau’s Fermi liquid theory. While thorough study of transport modes has been done for standard three-dimensional Fermi liquids, an equally in-depth analysis for two dimensional Fermi liquids is lacking. In applying the Landau kinetic equation (LKE) to a two-dimensional Fermi liquid, we obtain unconventional behavior of the zero sound mode c 0 . As a function of the usual dimensionless parameter s = ω / q v F , we find two peculiar results: first, for | s | > 1 we see the propagation of an undamped mode for weakly interacting systems. This differs from the three dimensional case where an undamped mode only propagates for repulsive interactions and the mode experiences Landau damping for any arbitrary attractive interaction. Second, we find that regardless of interaction strength, a propagating mode is forbidden for | s | < 1. This is profoundly different from the three-dimensional case where a mode can propagate, albeit damped. In addition, we present a revised Pomeranchuk instability condition for a two-dimensional Fermi liquid as well as equations of motion for the fluid that follow directly from the LKE. In two dimensions, we find a constant minimum for all Landau parameters for ℓ ⩾ 1 which differs from the three dimensional case. Finally we discuss the effect of a Coulomb interaction on the system resulting in the plasmon frequency ω p exhibiting a crossover to the zero sound mode.Abstract Using the Landau kinetic equation to study the non-equilibrium behavior of interacting Fermi systems is one of the crowning achievements of Landau’s Fermi liquid theory. While thorough study of transport modes has been done for standard three-dimensional Fermi liquids, an equally in-depth analysis for two dimensional Fermi liquids is lacking. In applying the Landau kinetic equation (LKE) to a two-dimensional Fermi liquid, we obtain unconventional behavior of the zero sound mode c 0 . As a function of the usual dimensionless parameter s = ω / q v F , we find two peculiar results: first, for | s | > 1 we see the propagation of an undamped mode for weakly interacting systems. This differs from the three dimensional case where an undamped mode only propagates for repulsive interactions and the mode experiences Landau damping for any arbitrary attractive interaction. Second, we find that regardless of interaction strength, a propagating mode is forbidden for | s | < 1. This is profoundly different from the three-dimensional case where a mode can propagate, albeit damped. In addition, we present a revised Pomeranchuk instability condition for a two-dimensional Fermi liquid as well as equations of motion for the fluid that follow directly from the LKE. In two dimensions, we find a constant minimum for all Landau parameters for ℓ ⩾ 1 which differs from the three dimensional case. Finally we discuss the effect of a Coulomb interaction on the system resulting in the plasmon frequency ω p exhibiting a crossover to the zero sound mode.

arXiv:1912.02699Journal of Physics Condensed MatterApr 17, 20201 citation

Collective excitations in fermi systems

Viktor Mikhaĭlovich Galit︠s︡kiĭ

PhysicaDec 1, 19603 citations

Quantum and nonlocal coherent effects in Boltzmann gases

A. E. Meyerovich

Quantum coherent phenomena in Boltzmann gases are studied on the basis of the generalized Waldmann-Snider kinetic equation. The equation takes into account the effects of quantum identity of particles. The conditions are formulated for the propagation of different collective modes in gases of particles with arbitrary internal degrees of freedom. Collective coherent effects are macroscopic manifestations of the molecular field for the transverse (off-diagonal) elements of particle distribution in a ``polarized'' system (a system with a nonuniform population of internal energy levels in an unperturbed state). The simplest results are obtained for particles with equidistant internal-energy levels exploiting the analogy with spin-polarized quantum gases. The accurate study of nonlocal interaction terms permits one to compare classical-kinetic and Fermi-liquid approaches to kinetic phenomena in dilute gases, and shows the limitations of both approaches. In the case of collective modes, more accurate schemes of derivation of the kinetic equation must be accompanied by the simultaneous calculations of nonlocal contributions.Quantum coherent phenomena in Boltzmann gases are studied on the basis of the generalized Waldmann-Snider kinetic equation. The equation takes into account the effects of quantum identity of particles. The conditions are formulated for the propagation of different collective modes in gases of particles with arbitrary internal degrees of freedom. Collective coherent effects are macroscopic manifestations of the molecular field for the transverse (off-diagonal) elements of particle distribution in a ``polarized'' system (a system with a nonuniform population of internal energy levels in an unperturbed state). The simplest results are obtained for particles with equidistant internal-energy levels exploiting the analogy with spin-polarized quantum gases. The accurate study of nonlocal interaction terms permits one to compare classical-kinetic and Fermi-liquid approaches to kinetic phenomena in dilute gases, and shows the limitations of both approaches. In the case of collective modes, more accurate schemes of derivation of the kinetic equation must be accompanied by the simultaneous calculations of nonlocal contributions.

Physical review. B, Condensed matterMay 1, 198920 citations

l.

We focus on the strength function and fragmentation width of the vibrations. We determine the contributions to the collective strength function which are associated with different values of relevant single-particle angular momentum. Applications to the nuclear isoscalar vibrations with multipolarities

L=0,

2, and 3 are presented.