Density Functional Theory of Spin-Polarized Disordered Quantum Dots

Using density functional theory, we investigate fluctuations of the ground-state energy of spin-polarized, disordered quantum dots in the metallic regime. To compare to experiment, we evaluate the distribution of addition energies and find a convolution of the Wigner-Dyson distribution, expected for noninteracting electrons, with a narrower Gaussian distribution due to interactions. The third moment of the total distribution is independent of interactions, and so is predicted to decrease by a factor of (2−5π/8)/(2−6/π) ≃ 0.405 upon application of a magnetic field, which transforms from the Gaussian orthogonal to the Gaussian unitary ensemble. PACS numbers: 73.61.-r, 73.23.Hk, 71.15.Mb