Screening of classical charges in quantum Coulomb systems.

Abstract

We show that the imaginary-time Green's functions of a system of quantum charged particles at equilibrium satisfy a set of sum rules which express the screening of a classical external charge. We also provide a new derivation of the perfect screening property ${\mathrm{lim}}_{\mathrm{k}\ensuremath{\rightarrow}0}$${\mathrm{\ensuremath{\epsilon}}}^{\mathrm{\ensuremath{-}}1}$(k)=0 where \ensuremath{\epsilon}(k) is the static dielectric function. The proof relies on exact equations for the Green's functions and certain assumptions of spatial clustering. It is nonperturbative, independent of the statistics, and applies to jellium as well as to multicomponent systems.