  Time-dependent (TD) density functional theory (TDDFT) promises a numerically
tractable account of many-body electron dynamics provided good simple
approximations are developed for the exchange-correlation (XC) potential
functional (XCPF). The theory is usually applied within the adiabatic XCPF
approximation, appropriate for slowly varying TD driving fields. As the
frequency and strength of these fields grows, it is widely held that memory
effects kick in and the eligibility of the adiabatic XCPF approximation
deteriorates irreversibly. We point out however that when a finite system of
electrons in its ground-state is gradually exposed to a very a high-frequency
and eventually ultra-strong homogeneous electric field, the adiabatic XCPF
approximation is in fact rigorously applicable. This result not only helps to
explain recent numerical results for a 1D-helium atom subject to a strong
linearly-polarized laser pulse (Thiel et al, Phys. Rev. Lett. 100, 153004,
(2008)) but also shows that it is applicable to any number of electrons and in
full 3D.
