Abstract
Growth rates of modes and associated behavior in a Fermi liquid unstable to density fluctuations are studied by using Landau theory. The hydrodynamic and collosionless limits (the latter treated by the Landau kinetic equation) are contrasted. These limits are bridged by treating the collision integral in the relaxation-time approximation. Approximate analytic expressions and numerical results are given for complex frequencies and growth rates, and the angular dependence of the quasiparticle distribution functions, for a variety of values of Landau parameters and the mean free path. The time development of the quasiparticle distribution function is calculated for arbitrary initial conditions. Growth rates close to the collisionless and hydrodynamic limits are also calculated using a completely general form of the collision integral.
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