Sum rules for inhomogeneous Coulomb systems

摘要

Using the stationary equilibrium BBGKY hierarchyandsome weak spatial decay properties of the correlations, we derive exact sum rules for the equilibrium distribution functions of ionic systems. Our results apply to both homogeneous and nonuniform systems. They show thatwhenthere is decay in such systems,thenthe total excess charge in the vicinity of a given number of fixed ions is zero, and that this excess charge has no dipole nor quadrupole moment. The implications for the static structure factor and for the dielectric tensor are discussed.