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##### The electron gas in TDDFT and SCDFT

**Authors**: M.A.L. Marques, and E.K.U. Gross

**Ref.**: Proceedings of the International School of Physics "Enrico Fermi", Course CLVII: The electron liquid paradigm in condensed matter physics, ed. by G.F. Giuliani and G. Vignale, 127-167 (2004)

**Abstract**: Summary. -- In this article we will give an overview of two extensions of ground state density functional theory (DFT) time-dependent DFT (TDDFT), and DFT for superconductors (SCDFT) and their interplay with the electron gas. TDDFT can be viewed as an alternative formulation of time-dep endent quantum mechanics that uses the electronic density as the basic variable. This theory is capable of tackling many-electron systems under the influence of a generic time-dependent external
potential (such as a laser field). Furthermore, TDDFT is a very powerful tool to calculate linear excitation spectra. On the other hand, SCDFT is an attempt to describe the phenomenon of superconductivity from a density functional perspective.
In all these density functional theories, the complexities of the many-body problem are included in the so-called exchange-correlation functional. This is a very complicated quantity that has to be approximated in any practical application of the
theory. One of the most successful approximate exchange-correlation functionals is certainly the local density approximation, which uses information from the uniform electron gas to construct an exchange-correlation functional for the inhomogeneous
system. Local density approximations have been proposed both within TDDFT and SCDFT. We will pay particular attention to their construction and, whenever possible, give a critical account of their successes and failures.

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