Landau Fermi Liquid Picture of Spin Density Functional Theory: Strutinsky Approach to Quantum Dots

We analyze the ground state energy and spin of quantum dots obtained from spin density functional theory (SDFT) calculations. First, we introduce a Strutinsky-type approximation, in which quantum interference is treated as a correction to a smooth Thomas-Fermi description. For large irregular dots, we find that the second-order Strutinsky expressions have an accuracy of about 5 percent compared to the full SDFT and capture all the qualitative features. Second, we perform a random matrix theory/random plane wave analysis of the Strutinsky SDFT expressions. The results are statistically similar to the SDFT quantum dot statistics. Finally, we note that the second-order Strutinsky approximation provides, in essence, a Landau Fermi liquid picture of spin density functional theory. For instance, the leading term in the spin channel is simply the familiar exchange constant. A direct comparison between SDFT and the perturbation theory derived ``universal Hamiltonian'' is thus made possible.