Relaxation of some fermion nonequilibrium momentum distributions

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Abstract
We study the time evolution of some momentum distributions for an infinite, dilute, and spatially homogeneous system of fermions by solving the Uehling-Uhlenbeck equation. The initial nonequilibrium distributions examined are (i) a Fermi sphere with an outer spherical shell, and (ii) a Fermi bisphere. It is found that the entropy of the system approaches its equilibrium value in a nearly exponential manner. Such a behavior allows an extraction of the relaxation times. The relaxation times decrease with increasing size of perturbation and depend on the shape of the perturbation. Deviations from equilibrium in the initial momentum distribution persist into the late stages of the relaxation process.