Sum rules and dynamical properties of two-dimensional classical electron liquid

Abstract

Expressions for the fourth frequency moment sum rule for the longitudinal and transverse current correlation functions are obtained for a classical system of electrons trapped on the surface of liquid helium. The expressions involving static triplet correlation functions are considerably simplified so that the numerical results for the moments can be easily obtained for all momentum transfers. The results for the moments as a function of wavenumber k are presented for 2.23 < or= Gamma < or=90.0. The authors make use of these results to analyse the recent molecular dynamics (MD) data on the dynamical structure function S(k, omega ) and the transverse current correlation function C_t(k, omega ) using the Mori formalism. It is found that a relaxation kernel essentially with single decay constant provides an overall good description of MD data over the entire range of Gamma.