Ground state energy of large atoms and quantum dots

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.