Anderson orthogonality catastrophe in realistic quantum dots

TL;DR

This paper investigates the Anderson orthogonality catastrophe in realistic quantum dots, revealing how degeneracies and shell structures influence many-body overlaps and their decay, with implications for mesoscopic systems.

Contribution

It provides new insights into how degeneracies and shell effects in quantum dots modify AOC, extending understanding beyond metallic and chaotic quantum dot models.

Findings

AOC is incomplete in finite quantum dots with broad overlap distributions.

Degeneracies and shell structures significantly affect AOC behavior.

Power law decay of overlaps is altered by energy level rearrangements.

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.