  Time-dependent quantities are calculated in the linear response limit for a
correlated one dimensional model atom driven by an external quadrupolar
time-dependent field. Besides the analysis of the time-evolving energy change
in the correlated two-particle system, and orthogonality of initial and final
states, Mehler's formula is applied in order to derive a point-wise
decomposition of the time-dependent one-matrix in terms of time-dependent
occupation numbers and time-dependent orthonormal, natural orbitals. Based on
such exact spectral decomposition on the time domain, R\'enyi's entropy is also
investigated. Considering the structure of the exact time-dependent one-matrix,
an independent-particle model is defined from it which contains exact
information on the single-particle probability density and probability current.
The resulting noninteracting auxiliary state is used to construct an effective
potential and discuss its applicability.
