Time-dependent local density formalism

Concurrent with these developments, the density functional formalism has emerged as an alternative to a Hartree Fock based description of the electronic structure of atoms, molecules and solids. In its most common form as a local density approximation (LDA) the question of atomic photoionization can again be addressed. Here too, one finds that the simplest approach falls to adequately charr-. acterize the experimental results in many cases. However, a recent straightforward generalization of density functional theory to time-dependent phenomena has been applied successfully to the problem of the optical response of atoms. In particular, highly accurate photoionization cross sections can be readily obtained. The purpose of the present article is to review this time-dependent local density approximation (TDLDA), illustrate its scope and limitations and compare it to the more familiar Hartree-Fock based methods. 

TIME-DEPENDENT LOCAL DENSITY APPROXIMATION Formalism... 

The local mobility A in general depends on the environment. In the simplest model (local coupling approximation), A is assumed to be a constant related to an effective diffusion coefficient D . This assumption is valid when the segment density fluctuations are small compared to the average densities o. Another simple modd is to assume that A depends on the segment density as A =Ao< (r,t), where Aq is a constant. The formal theory of time evolution of density variables with general kinetic coeffidents was developed by Kawasaki and Sddmoto, but this is rather difficult to implement in practice. 

We mention that there are other noteworthy single excited-state theories the stationary-principle theory of Gorling [33], the formalism of Sahni [34] or the local scaling approach of Ludena and Kryachko [35]. Beyond the time-independent theories mentioned above the time-dependent density functional theory [36] provides... 

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