Interacting electrons in a 2D quantum dot

TL;DR

This paper performs exact numerical diagonalization of a 2D quantum dot with 2-4 electrons, comparing results with perturbation theory and classical predictions, revealing good agreement in different regimes.

Contribution

It provides a detailed numerical analysis of interacting electrons in a 2D quantum dot, highlighting the agreement with perturbation theory and classical models across parameter ranges.

Findings

Numerical results agree with perturbation theory for small coupling constants.

Diagonalization results match classical predictions for large coupling constants.

The study offers insights into electron interactions in quantum dots across different regimes.

Abstract

The exact numerical diagonalization of the Hamiltonian of a 2D circular quantum dot is performed for 2, 3, and 4 electrons.The results are compared with those of the perturbation theory.Our numerical results agree reasonably well for small values of the dimensionles coupling constant \lambda=a\over a_B where a is the dot radius and a_B is the effective Bohr radius.Exact diagonalization results are compared with the classical predictions, and they are found to be almost coincident for large \lambda values. PACS Numbers: 73.20.Dx, 73.61.-r