The Keldysh Formalism Applied to Time-Dependent Current-Density-Functional Theory
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- van Leeuwen R. (2003) The Keldysh Formalism Applied to Time-Dependent Current-Density-Functional Theory. In: Gidopoulos N.I., Wilson S. (eds) The Fundamentals of Electron Density, Density Matrix and Density Functional Theory in Atoms, Molecules and the Solid State. Progress in Theoretical Chemistry and Physics, vol 14. Springer, Dordrecht
In this work we demonstrate how to derive the Kohn-Sham equations of time-dependent current-density functional theory from a generating action functional defined on a Keldysh time contour. These Kohn-Sham equations contain an exchange-correlation contribution to the vector potential. For this quantity we derive an integral equation. We further derive an integral equation for its functional derivative, the exchangecorrelation kernel, which plays an essential role in response theory. The exchange-only limits of the latter equation is studied in detail for the electron gas and future applications are discussed.
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