Signatures of quantum chaos in mesoscopic many-body effects

Many-body effects have been a key interest in condensed matter physics for many years. We study them for mesoscopic, rather than for bulk, systems in the context of photoabsorption spectra (X-ray edge problem) and focus on deviations from the bulk (metallic) case as well as on quantum-chaos signatures such as the geometry-dependence of the photoabsorption cross section. It is determined by two counteracting many-body effects, known as Anderson orthogonality catastrophe and Mahan's exciton. They result from the system's many-body response to the sudden, localized perturbation given by the core hole that is left behind when the x-ray excites an electron. We find characteristic deviations from the metallic case that are strongest near the system boundary, as a result of the prominent correlation between the wave function (that drops to zero) and its derivative (that is correspondingly large). As a consequence, the photoabsorption cross section develops a pronounced peak, in contrast to a rounded signature for metals and a slight peak away from the system boundary. We furthermore study the dependence on the system geometry and find that level degeneracies, possible in ballistic quantum dots of regular, rather than chaotic, shape trigger considerable changes in the orthogonality catastrophe response that altogether becomes somewhat stronger.