Zero and First Sound in Normal Fermi Systems

TL;DR

This paper uses a moment method to analyze sound modes in normal Fermi systems, capturing zero and first sound, their crossover, and additional thermal and collective excitations across different regimes.

Contribution

It introduces a moment method approach to unify the description of zero and first sound in Fermi systems, including crossover behavior at finite temperatures.

Findings

Reproduces zero and first sound in extreme regimes

Describes crossover between collisionless and hydrodynamic regimes

Identifies additional thermal diffusion and collective modes

Abstract

On the basis of a moment method, general solutions of a linearized Boltzmann equation for a normal Fermi system are investigated. In particular, we study the sound velocities and damping rates as functions of the temperature and the coupling constant. In the extreme limits of collisionless and hydrodynamic regimes, eigenfrequency of sound mode obtained from the moment equations reproduces the well-known results of zero sound and first sound. In addition, the moment method can describe crossover between those extreme limits at finite temperatures. Solutions of the moment equations also involve a thermal diffusion mode. From solutions of these equations, we discuss excitation spectra corresponding to the particle-hole continuum as well as collective excitations. We also discuss a collective mode in a weak coupling case.