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Time-dependent density functional theory (TDDFT) has seen a surge of
applications in recent years, for the calculation of optical spectra and
response of atoms, molecules, clusters, and solids. But TDDFT not
limited to the linear response regime; its promise to describe electron
correlation in strong-field phenomena, including high-harmonic
generation, above-threshold ionization, and electronic quantum control
theory, is only beginning to be tapped. The non-perturbative regime is
where TDDFT is the only feasible scheme, as wavefunction methods for
even a few electrons are prohibitively expensive.
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Although in principle an exact theory, the functionals of TDDFT must in
practise be approximated. I will discuss certain properties of the exact
functional that are essential for approximations to satisfy in order to
capture the dynamics accurately in strong fields. Some of these are
particularly challenging to incorporate into functional approximations,
for example history-dependence and initial-state-dependence, critical
for attosecond quantum control phenomena. I will present a new extension
to phase-space density functionals, which may turn out to be a more
natural framework for these problems.
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