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Abstract
We discuss the model of a D-dimensional confined electron gas in which the particles are trapped by a harmonic potential. In particular, we study the non-interacting kinetic and exchange energies of finite-size inhomogeneous systems, and compare the resulting Thomas–Fermi and Dirac coefficients with various uniform electron gas paradigms. We show that, in the thermodynamic limit, the properties of this model are identical to those of the D-dimensional Fermi gas.
Acknowledgements
We thank Joshua Hollett for useful discussions, the NCI National Facility for a generous grant of supercomputer time and the Australian Research Council (Grants DP0984806, DP1094170 and DP120104740) for funding.
Notes
1. This generalizes our earlier work Citation27 in which ‘D-spherium’ was a two-electron system Citation47–49.
2. We adopt the convention that a D-sphere is the surface of a (D + 1)-dimensional ball.
3. Anisotropy effects can be taken into account using the methodology developed in Citation50.