A Generalised Linear Response Theory applied to the Dielectric Function of Coulomb Systems

Abstract

A generalised linear response theory is used to derive the dielectric function at arbitrary wave numbers k and frequencies w for interacting quantum systems. The connection to thermodynamic Green functions allows the systematic perturbative treatment going beyond RPA and treating local field corrections as well as the inclusion of collisions on the same footing. Emphasis will be on the demonstration of the formalism. Results will be presented for the three-dimensional as well as two-dimensional case of an interacting electron gas. In the long-wavelength limit, a Drude-type expression with frequency dependent relaxation time is given bridging the theories of dielectric function and electrical conductivity.