Ground state energy of large atoms and quantum dots

TL;DR

This paper analyzes the ground state energy of large atoms and quantum dots, revealing dominant semiclassical Hartree-Fock contributions, correlation effects, and energy oscillations linked to classical particle dynamics, including chaotic cases.

Contribution

It provides a detailed computation of correlation effects and energy oscillations, including in systems with chaotic classical dynamics, extending previous semiclassical analyses.

Findings

Dominant energy terms are semiclassical Hartree-Fock predictions.

Correlation effects appear at order N ln N for atoms and N for quantum dots.

Energy oscillations reflect classical particle dynamics, including chaos.

Abstract

We determine the ground state energy of atoms and quantum dots whose number N of electrons is large. We show that the dominant terms of the energy are those given by a semiclassical Hartree-Fock theory. Correlation effects appear at the order N ln N for atoms and the order N for quantum dots. We compute them. The semiclassical Hartree-Fock theory creates oscillations in the ground state energy as a function of N . These oscillations reflect the dynamics of a classical particle moving in the presence of the Thomas-Fermi potential. The dynamics is regular for atoms and some dots, but we present the case of a dot where this dynamics is fully chaotic and we compute the oscillating part of the ground state energy in this case.