| We study the response of integrable and chaotic mesoscopic systems to a sudden, localized perturbation caused, e.g., by an x-ray exciting a core electron into the conduction band. Anderson orthogonality catastrophe (AOC) refers to the disappearance of the overlap of the many-particle ground states before and after the perturbation is applied in the thermodynamic limit. In contrast, a finite number of particles causes AOC to be incomplete with a broad distribution of AOC overlaps originating from mesoscopic fluctuations, in particular those that occur close to the Fermi energy. We consider two integrable ballistic quantum dots (rectangle and disc with hard walls) subject to a rank-one perturbation and compare the results with those obtained for generic chaotic systems. We find that the distributions of AOC overlaps differ, especially in the presence of a magnetic field. Level degeneracies present in integrable systems lead to additional peaks in the AOC distribution that shift the average overlap to smaller values. Furthermore, we apply these results to study Fermi edge singularities in the photo-absorption spectra of mesoscopic systems and show that their signature can qualitatively deviate from metallic (bulk-like) systems. |
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