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- W2042484823 abstract "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 $Nensuremath{rightarrow}ensuremath{infty}$ 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 $Nmathrm{ln}N$ for atoms, in agreement with available data. For dots, they appear at the order $N$." @default.
- W2042484823 created "2016-06-24" @default.
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- W2042484823 date "2010-03-26" @default.
- W2042484823 modified "2023-10-03" @default.
- W2042484823 title "Atoms and quantum dots with a large number of electrons: The ground-state energy" @default.
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- W2042484823 doi "https://doi.org/10.1103/physreva.81.032122" @default.
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