Date: 11 Jun 2005

Density functional theory of time-dependent phenomena

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A density-functional formalism comparable to the theory of Hohenberg, Kohn and Sham is developed for electronic systems subject to time-dependent external fields. The formalism leads to a set of time-dependent Kohn-Sham equations which, in addition to the external potential, contain a time-dependent Hartree term and a local time-dependent exchange-correlation potential. Rigorous properties and explicit approximations of the latter are discussed in detail. Generalizations of the basic formalism to incorporate the nuclear motion and to deal with magnetic effects are described. Within the regime of linear-response theory, the time-dependent Kohn-Sham equations lead to a formally exact representation of the frequency-dependent linear density response. Applications within the linear-response regime include the computation of photoabsorbtion cross sections, the determination of van der Waals forces and the calculation of excitation energies. The latter is based on the fact that the frequency-dependent linear density response has poles at the true excitation energies of the interacting many-body system. The time-dependent Kohn-Sham formalism then leads to a simple additive correction of the Kohn-Sham single-particle excitation energies. Beyond the linear-response regime, the time-dependent Kohn-Sham scheme is applied to atoms in strong femto-second laser pulses to describe multi-photon ionization and harmonic generation in a non-perturbative way.