  We calculate the frequency-dependent equilibrium noise of a mesoscopic
capacitor in time-dependent density functional theory (TDDFT). The capacitor is
modeled as a single-level quantum dot with on-site Coulomb interaction and
tunnel coupling to a nearby reservoir. The noise spectra are derived from
linear-response conductances via the fluctuation-dissipation theorem. Thereby,
we analyze the performance of a recently derived exchange-correlation potential
with time-nonlocal density dependence in the finite-frequency linear-response
regime. We compare our TDDFT noise spectra with real-time perturbation theory
and find excellent agreement for noise frequencies below the reservoir
temperature.
