  We study Anderson orthogonality catastrophe (AOC) for an parabolic quantum
dot (PQD), one of the experimentally realizable few-electron systems. The
finite number of electrons in PQD causes AOC to be incomplete, with a broad
distribution of many-body overlaps. This is a signature of mesoscopic
fluctuations and is in agreement with earlier results obtained for chaotic
quantum dots. Here, we focus on the effects of degeneracies in PQDs, realized
through their inherent shell structures, on AOC. We find rich and interesting
behaviours as a function of the strength and position of the perturbation, the
system size, and the applied magnetic field. In particular, even for weak
perturbations, we observe a pronounced AOC which is related to the degeneracy
of energy levels. Most importantly, the power law decay of the many-body
overlap as a function of increasing number of particles is modified in
comparison to the metallic case due to rearrangements of energy levels in
different shells.
