Dynamic Response of Inhomogeneous Fermi Systems

This paper presents a theory of the linear density response to an external time-dependent scalar potential for a Fermi system whose unperturbed density varies slowly. Simple local-density-functional response theory is valid except in a region of small $q$ and $\omega$ (wave number and frequency of the perturbation). For this region we have worked out a generalization, to the case of inhomogeneous systems of Landau Fermi-liquid theory.