Response function and plasmon dispersion for strongly coupled Coulomb liquids

Abstract

We present a new approach for the calculation of the dielectric response functions for various strongly coupled Coulomb systems, whose main common feature is that the charges are quasilocalized. Such a model is expected to be a valid description of a strongly coupled plasma in the \ensuremath{\Gamma}\ensuremath{\gg}1 limit. The dielectric function \ensuremath{\epsilon}(k\ensuremath{\omega}) and the longitudinal plasmon dispersion \ensuremath{\omega}(k) appear as functionals of the equilibrium pair-correlation functions. We derive the longitudinal-plasmon dispersions for arbitrary k values for the three- and two-dimensional one-component plasmas; both of them saturate after an oscillatory behavior substantially below their random-phase approximation value for large k values. In two-component systems correlational effects bring about marked upward and downward shifts in the plasma frequency \ensuremath{\omega}(k=0). We find good agreement with molecular-dynamics data for ${\mathrm{H}}^{+}$-${\mathrm{H}}^{2+}$ mixtures and predict a more significant shift for ${\mathrm{H}}^{+}$--high-Z mixtures.