Self-diffusion, conductivity, and long-wavelength plasma oscillations in strongly coupled two-component plasmas

The autocorrelation functions of the microscopic electric current $J\left(t\right)\mathrm{}$ and the electron velocity $Z_2\mathrm{}\left(t\right)\mathrm{}$ are calculated for strongly coupled, semiclassical two-component plasmas. The corresponding memory functions are expressed in terms of mode-coupling integrals involving density- and energy-correlation function in the framework of a microscopic kinetic theory which preserves the exact statics. Through a sequence of well-defined approximations, the expressions for the memory functions are made self-consistent, the resulting equations are solved iteratively with the interaction potentials, and the static-partial-structure factors as the only input. The theory is then applied to weakly degenerate hydrogen and carbon plasmas for values of the plasma parameter of order 1. The resulting correlational functions $J\left(t\right)\mathrm{}$ and $Z_2\mathrm{}\left(t\right)\mathrm{}$ and their integrals, the electrical conductivity, and the electron self-diffusion constant, agree reasonably well with the "molecular-dynamics" data of Hansen and McDonald and with additional simulation results presented here. The "long-time tail" in $J\left(t\right)\mathrm{}$ observed in the simulations is interpreted in terms of mode-coupling effects. The damping and frequency shift of the plasmon peak in the dynamical charge-fluctuation spectrum are explicity evaluated in the long-wavelength limit; the frequency shift above the plasma frequency is shown to be nonnegligible for strong coupling.