Zero and First Sound in Normal Fermi Systems

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.Comment: 38 pages, 5 figure

Density and spin modes in imbalanced normal Fermi gases from collisionless to hydrodynamic regime

“…As discussed in Ref. [17], our moment method in the collisionless limit can reproduce the results given by the random phase approximation in the long-wavelength regime.…”

“…is positioned in the continuum [17]. However, if we calculate the dynamic structure factor, the structure of the collective mode can be clearly seen.…”

“…We derive a moment equation from a linearized Boltzmann equation for a two-component mass and population imbalanced normal Fermi gas by extending formulation for a mass and population balanced normal Fermi case [17,18]. Let σ =↑ or ↓ be a pseudo-spin describing each component of the Fermi gas with an atomic mass m σ .…”

“…In this Appendix, we consider the collective mode in the collisionless regime at an extremely low temperature T ≪ min(T F,↑ , T F,↓ ), by extending the study for the zero sound in the mass and population balanced gas [15][16][17]. In this case, from (B4), (B5), and (B6), one can takẽ a σ = ν σ,0 /W σ,0 , |b| = σ pν σ,1 / σ W σ,2 as well as c σ = 0, because of relations at T = 0, given by…”

Kinetic modelling of the quantum gases in the normal phase

“…Applying the Chapman-Enskog expansion (Chapman & Cowling 1970) to the semi-classical Boltzmann equation (Kavoulakis et al 2000;Watabe et al 2010), one obtains the thermal conductivity as…”