Atoms and quantum dots with a large number of electrons: The ground-state energy
- 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, Vol. 81, Issue 3; Other Information: DOI: 10.1103/PhysRevA.81.032122; (c) 2010 The American Physical Society; ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
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CHAOS THEORY
CORRELATIONS
COULOMB FIELD
ELECTRONS
FUNCTIONS
GROUND STATES
HAMILTONIANS
NUCLEI
OSCILLATIONS
POTENTIALS
QUANTUM DOTS
SEMICLASSICAL APPROXIMATION
SHAPE
THOMAS-FERMI MODEL
APPROXIMATIONS
ATOMIC MODELS
CALCULATION METHODS
ELECTRIC FIELDS
ELEMENTARY PARTICLES
ENERGY LEVELS
FERMIONS
LEPTONS
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MATHEMATICS
NANOSTRUCTURES
QUANTUM OPERATORS