| We study the Anderson orthogonality catastrophe (AOC) for parabolic quantum dots (PQD). AOC is one of the many-body responses leading to Fermi-edge singularities in, e.g., the photo-absorption cross-section of metals. We use rank-one perturbation to model the static impurity created by an x-ray exciting a core electron of a PQD into the conduction band. A PQD is characterized by an inherent shell structure. The degeneracy in a shell is slightly lifted in presence of a weak magnetic field (almost degenerate case). The behavior of a PQD is governed by two energy-scales: The inter-shell spacing (set by the oscillator¢s bare frequency) and the intra-shell level spacing (set by the applied magnetic field). We study the statistics of the Anderson overlap for an uniform as well as a realistic mesoscopic PQD as a function of perturbation strength, position of the localized impurity, number of electrons and system size. The clustering of levels in shells gives rise to an oscillatory behaviour in Anderson overlap as a function of filling of the PQD levels. In particular, we find a pronounced AOC, related to the (near) degeneracy of levels, whenever a new shell is opened up. This inherent shell structure survives in the presence of mesoscopic fluctuations, when we observe the value of the Anderson overlap remains unchanged despite adding several electrons to the system. A similar bunching phenomenon has been observed in transport measurements on quantum dots with up to 200 electrons by Zhitenev et.al.[PRL,79, 2308 (1997)], and we discuss a possible connection to our findings. |
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