Statistical mechanics of dense ionized matter. V. Hydrodynamic limit and transport coefficients of the classical one-component plasma

We study the static and dynamical correlations of density fluctuations in a classical one-component plasma (OCP), in the framework of thermodynamic fluctuation theory and linearized hydrodynamics. First we show that the fluctuations of the local electric field stabilize the OCP against density fluctuations, even when the compressibility becomes negative for $\Gamma \gtrsim 3$, where $\Gamma$ is the usual plasma coupling parameter. Then, following closely the work of Mountain, we compute the dynamical structure factor in the hydrodynamic limit and show that the thermal Rayleigh peak vanishes in the long-wavelength limit, in agreement with recent molecular dynamics results. The shear and bulk viscosity coefficients $\eta$ and $\zeta$ are calculated for large $\Gamma$ in the framework of the "generalized hydrodynamics" formalism, using the known short-time expansion of the correlation functions. The coefficient $\eta$ is found to exhibit a minimum as a function of $\Gamma$ and $\zeta$ is found to be negligible compared to $\eta$ in the OCP.