Kinetic theory of the shear viscosity of a strongly coupled classical one-component plasma

We present an approximation to the linearized collision operator or memory function of the exact kinetic equation obeyed by the correlation function of the phase-space density of a classical one-component plasma. This approximate collision operator generalizes the well known Balescu-Guernsey-Lenard (BGL) operator to finite wavelengths, finite frequencies, and finite coupling constants. It, moreover, satisfies the necessary symmetry relations, leads to appropriate conservation laws, and fulfills its first sum rule exactly. Next we use this operator to compute the shear viscosity $\eta$ for a series of coupling constants spanning the whole fluid phase. For weak coupling we make contact with the BGL theory, while for strong coupling we confirm, at least qualitatively, the results of Vieillefosse and Hansen, who predicted a minimum in $\eta$ as a function of temperature. We also demonstrate the important role played by the sum rules in the quantitative evaluation of a transport coefficient such as $\eta$.