Dynamical properties of a two-dimensional Coulomb fluid

Simplified expressions for the fourth-frequency-moment sum rules for the longitudinal- and transverse-current correlation functions have been obtained for a two-dimensional classical Coulomb fluid interaction with a logarithmic potential. The numerical results for these sum rules are presented as a function of wavenumber k for Gamma =2, 10 and 40. Using the exact result for the triplet correlation function for Gamma =2, it is found that the error involved in the use of the superposition approximation is about 5% for 0.4 < or=k < or=4.0. Sum rules and a simple mean-field theory are used to study the plasma wave dispersion for Gamma =72. Results are in close agreement with recent molecular dynamics calculations