Energy Spectra of Few-Electron Quantum Dots

TL;DR

This paper develops a renormalized perturbation approach to analyze the energy spectra of few-electron quantum dots, successfully bridging quantum and semiclassical regimes and demonstrating accuracy across various parameters.

Contribution

It introduces a novel renormalized perturbation series for quantum dot energy spectra with 2-5 electrons, covering ground and excited states, and classifies asymptotic energy levels.

Findings

Accurate energy spectra across electron numbers and parameters.

Energy levels transition from quantum to semiclassical behavior.

More electrons lead to more classical system behavior.

Abstract

We present the renormalized perturbation series for the energy spectrum of the parabolic quantum dot with 2 -- 5 electrons considering ground and the lowest excited states. The proper classification of asymptotic energy levels is performed and behaviour of energy levels from quantum to semiclassical regime is traced. Comparison between the present results and those of exact numerical Hamiltonian diagonalization shows a fair accuracy of the proposed method over the whole range of the electron-electron coupling constant and magnetic field values. The obtained results indicate that increasing of the number of electrons in a dot leads to more classic behaviour of the system.