Fermi Edge Singularities in the Mesoscopic Regime: II. Photo-absorption Spectra

We study Fermi edge singularities in photo-absorption spectra of generic mesoscopic systems such as quantum dots or nanoparticles. We predict deviations from macroscopic-metallic behavior and propose experimental setups for the observation of these effects. The theory is based on the model of a localized, or rank one, perturbation caused by the (core) hole left behind after the photo-excitation of an electron into the conduction band. The photo-absorption spectra result from the competition between two many-body responses, Anderson's orthogonality catastrophe and the Mahan-Nozieres-DeDominicis contribution. Both mechanisms depend on the system size through the number of particles and, more importantly, fluctuations produced by the coherence characteristic of mesoscopic samples. The latter lead to a modification of the dipole matrix element and trigger one of our key results: a rounded K-edge typically found in metals will turn into a (slightly) peaked edge on average in the mesoscopic regime. We consider in detail the effect of the "bound state" produced by the core hole.