Theory of strongly correlated charged-particle systems: Plasma turbulence and high-density electron liquids

A unified theory is developed for describing dynamic and static properties of strongly correlated charged-particle systems, such as a high-density electron liquid and a strongly turbulent plasma, for which the correlation (or fluctuation) energy is comparable in magnitude to the kinetic energy. Based on the microscopic Klimontovich formalism, a systematic renormalization of the single-particle propagators is carried out and vertex corrections arising from strong correlations are taken account of. The resulting theory is examined, and found to be satisfactory, in the light of a number of rigorous criteria, such as explicit inclusion of statistical modification effects in the single-particle orbits, dynamic modification of effective particle interactions brought about by strong correlations, frequency-moment sum rules of the dielectric response function, and reproduction of exact results known in the static properties of the electron liquid; the theory is thus valid for all wave numbers and frequencies. With the aid of a velocity-average approximation, we show that the result can be expressed in a simplified form which still satisfies those criteria. Its relation with the polarization potential model in the theory of condensed matter is thereby noted; explicit expressions for the scalar and vector polarization potentials, the wave-number-dependent effective mass, and the collisional contribution to the response function are obtained.