Atoms and quantum dots with a large number of electrons: The ground-state energy

Journal Article · Mon Mar 15 04:00:00 EDT 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.81.032122· OSTI ID:21408381

Kunz, Herve; Rueedi, Rico ^[1]

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1. Institute of Theoretical Physics, Ecole Polytechnique Federale de Lausanne (EPFL), CH-1015 Lausanne (Switzerland)

We compute the ground-state energy of atoms and quantum dots with a large number N of electrons. Both systems are described by a nonrelativistic Hamiltonian of electrons in a d-dimensional space. The electrons interact via the Coulomb potential. In the case of atoms (d=3), the electrons are attracted by the nucleus via the Coulomb potential. In the case of quantum dots (d=2), the electrons are confined by an external potential, whose shape can be varied. We show that the dominant terms of the ground-state energy are those given by a semiclassical Hartree-exchange energy, whose N{yields}{infinity} limit corresponds to Thomas-Fermi theory. This semiclassical Hartree-exchange 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 in general in the case of dots, the motion contains a chaotic component. We compute the correlation effects. They appear at the order NlnN for atoms, in agreement with available data. For dots, they appear at the order N.

• OSTI ID: 21408381
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 3 Vol. 81; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
APPROXIMATIONS
ATOMIC MODELS
ATOMS
CALCULATION METHODS
CHAOS THEORY
CORRELATIONS
COULOMB FIELD
ELECTRIC FIELDS
ELECTRONS
ELEMENTARY PARTICLES
ENERGY LEVELS
FERMIONS
FUNCTIONS
GROUND STATES
HAMILTONIANS
LEPTONS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MATHEMATICS
NANOSTRUCTURES
NUCLEI
OSCILLATIONS
POTENTIALS
QUANTUM DOTS
QUANTUM OPERATORS
SEMICLASSICAL APPROXIMATION
SHAPE
THOMAS-FERMI MODEL