Dynamic spectral aspects of interparticle correlation

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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, Rényi'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.