Electron interactions, classical integrability, and level statistics in quantum dots

TL;DR

This paper investigates how electron interactions influence the spectral properties and classical integrability of quantum dots, revealing that interactions induce non-integrability and affect level statistics.

Contribution

It establishes a connection between electron interactions in quantum dots and classical integrability, demonstrating how interactions break integrability and alter spectral behavior.

Findings

Interactions make the classical system non-integrable.

Spectral properties depend on interaction strength and magnetic fields.

Classical-quantum correspondence elucidates level statistics changes.

Abstract

The role of electronic interactions in the level structure of semiconductor quantum dots is analyzed in terms of the correspondence to the integrability of a classical system that models these structures. We find that an otherwise simple system is made strongly non-integrable in the classical regime by the introduction of particle interactions. In particular we present a two-particle classical system contained in a $d$-dimensional billiard with hard walls. Similarly, a corresponding two-dimensional quantum dot problem with three particles is shown to have interesting spectral properties as function of the interaction strength and applied magnetic fields.