Anderson orthogonality catastrophe in realistic quantum dots

Abstract

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.