Fermi-Edge Singularities in the Mesoscopic X-Ray Edge Problem

We study the x-ray edge problem for a chaotic quantum dot or nanoparticle displaying mesoscopic fluctuations. In the bulk, x-ray physics is known to produce deviations from the naively expected photoabsorption cross section in the form of a peaked or rounded edge. For a coherent system with chaotic dynamics, we find substantial changes and in particular that a photoabsorption cross section showing a rounded edge in the bulk will change to a slightly peaked edge on average as the system size is reduced to a mesoscopic (coherent) scale.