  We propose a scheme to extract the many-body spectral function of an
interacting many-electron system from an equilibrium density functional theory
(DFT) calculation. To this end we devise an ideal STM-like setup and employ the
recently proposed steady-state DFT formalism (i-DFT) which allows to calculate
the steady current through a nanoscopic region coupled to two biased
electrodes. In our setup one of the electrodes serves as a probe ('STM tip'),
which is weakly coupled to the system we want to measure. In the ideal STM
limit of vanishing coupling to the tip, the system is restored to
quasi-equilibrium and the normalized differential conductance yields the exact
equilibrium many-body spectral function. Calculating this quantity from i-DFT,
we derive an exact relation expressing the interacting spectral function in
terms of the Kohn-Sham one. As illustrative examples we apply our scheme to
calculate the spectral functions of two non-trivial model systems, namely the
single Anderson impurity model and the Constant Interaction Model.
