Microscopic theory of the long-wavelength modes of two-component plasmas and ionic liquids: II. The longitudinal modes

The modification of the damping rate of the sound modes by Coulomb phenomena is demonstrated from first principles. The heat modes of one- and two-component systems of charged particles are shown to differ by a factor c_p/c_v. Microscopic expressions for the interspecies energy and longitudinal momentum relaxation frequencies are provided. The charge relaxation modes are shown to reduce in the limit of weak-coupling to a pair of plasma oscillations occurring slightly below the plasma frequency while being slightly damped even at infinite wavelength. In the opposite limit of strong-coupling the same pair of charge relaxation modes is shown to split into an interspecies momentum relaxation mode and an approximate hydrodynamic diffusion mode. An Einstein relation between the diffusion constant and the electric conductivity is also demonstrated. All expressions are obtained for arbitrary density and coupling.