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Recent work showed that the exact exchange-correlation potential oftime-dependent density functional theory generically displays dynamical stepstructures. These have a spatially non-local and time-non-local dependence onthe density in real time dynamics. The steps are missing in the usualapproximations which consequently yield inaccurate dynamics. Yet these sameapproximations typically yield good linear response spectra. Here weinvestigate whether the steps appear in the linear response regime, when theresponse is calculated from a real-time dynamics simulation, by examining theexact correlation potential of model two-electron systems at various times. Wefind there are no step structures in regions where the system response islinear. Step structures appear in the correlation potential only in regions ofspace where the density response is non-linear; these regions, havingexponentially small density, do not contribute to the observables measured inlinear response.

Absence of Dynamical Steps in the Exact Correlation Potential in Linear Response