Dynamical theory of strongly coupled two-dimensional Coulomb fluids in the weakly degenerate quantum domain

We study the problem of dynamical response and plasma mode dispersion in strongly coupled two-dimensional Coulomb fluids (2DCFs) in the weakly degenerate quantum domain. Adapting the nonlinear response function approach of Golden and Kalman [Phys. Rev. A 19, 2112 (1979)] to the 2DCF, we construct a self-consistent approximation scheme for the calculation of the density response functions and plasma mode dispersion at long wavelengths. The basic ingredients in the construction are (i). the first kinetic equation in the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy, (ii). the velocity-average-approximation (VAA) hypothesis, (iii.) the quadratic fluctuation-dissipation theorem, and (iv). the dynamical superposition approximation (DSA) closure hypothesis. The reliability of the VAA-DSA theory can be assessed by observing that the principal coupling correction to the 2D temperature-dependent Lindhard function is identified as being precisely the part of the third-frequency-moment sum-rule coefficient proportional to the potential energy.