  Many-body phenomena, a key interest in the investigation of bulk solid state
systems, are studied here in the context of the x-ray edge problem for
mesoscopic systems. We investigate the many-body effects associated with the
sudden perturbation following the x-ray excitation of a core electron into the
conduction band. For small systems with dimensions at the nanoscale we find
considerable deviations from the well-understood metallic case where Anderson
orthogonality catastrophe and the Mahan-Nozieres-DeDominicis response cause
characteristic deviations of the photoabsorption cross section from the naive
expectation. Whereas the K-edge is typically rounded in metallic systems, we
find a slightly peaked K-edge in generic mesoscopic systems with
chaotic-coherent electron dynamics. Thus the behavior of the photoabsorption
cross section at threshold depends on the system size and is different for the
metallic and the mesoscopic case.
