Plasma mode of weakly and strongly coupled one-component plasmas

Starting from a novel exact expression for the dielectric constant of a classical one-component plasma, we study the important modifications of the plasma oscillation modes which appear when one progressively increases the plasma expansion parameter $\lambda$. For small $\lambda$ values the evaluation of the plasma mode requires a non-Markovian theory. We find good agreement between our results, recent computer findings, and known theoretical expressions. For instance, the dispersion of the plasma frequency is shown to take on values slightly above the mean-field prediction. For large $\lambda$ values the plasma mode is shown to be expressible in terms of hydrodynamical quantities. Here the dispersion of the plasma frequency is shown to be negative, while the damping of the plasma mode is given by the strong-coupling limit of the longitudinal viscosity from which the non-Markovian contributions to the bulk viscosity are to be deleted.