Collective Behavior of Stable and Unstable Hot Fermi Systems

Abstract

We calculate the density response of an interacting Fermi system at finite temperature from a generalization of Landau′s kinetic equation for quasiparticles. Detailed calculations are made for a form of the interaction function, ƒpp′, that allows for scalar and vector molecular fields. Collisions between quasiparticles are treated in a relaxation-time approximation. The dispersion relation for sound waves in hot Fermi liquids is derived and analytical formulae are found in the hydrodynamic, collisionless, and low temperature limits. We consider, in addition to cases where the system is stable, situations where the system is unstable with respect to formation of density waves. The general case is solved numerically for a selected set of Landau parameters, relaxation times, and temperatures.